[sql] Import reference version of SQLite 3.8.7.4.

third_party/sqlite/sqlite-src-3080704/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 responsible for
+** generating the code that loops through a table looking for applicable
+** rows.  Indices are selected and used to speed the search when doing
+** so is applicable.  Because this module is responsible for selecting
+** indices, you might also think of this module as the "query optimizer".
+*/
+#include "sqliteInt.h"
+#include "whereInt.h"
+
+/*
+** Return the estimated number of output rows from a WHERE clause
+*/
+u64 sqlite3WhereOutputRowCount(WhereInfo *pWInfo){
+  return sqlite3LogEstToInt(pWInfo->nRowOut);
+}
+
+/*
+** Return one of the WHERE_DISTINCT_xxxxx values to indicate how this
+** WHERE clause returns outputs for DISTINCT processing.
+*/
+int sqlite3WhereIsDistinct(WhereInfo *pWInfo){
+  return pWInfo->eDistinct;
+}
+
+/*
+** Return TRUE if the WHERE clause returns rows in ORDER BY order.
+** Return FALSE if the output needs to be sorted.
+*/
+int sqlite3WhereIsOrdered(WhereInfo *pWInfo){
+  return pWInfo->nOBSat;
+}
+
+/*
+** Return the VDBE address or label to jump to in order to continue
+** immediately with the next row of a WHERE clause.
+*/
+int sqlite3WhereContinueLabel(WhereInfo *pWInfo){
+  assert( pWInfo->iContinue!=0 );
+  return pWInfo->iContinue;
+}
+
+/*
+** Return the VDBE address or label to jump to in order to break
+** out of a WHERE loop.
+*/
+int sqlite3WhereBreakLabel(WhereInfo *pWInfo){
+  return pWInfo->iBreak;
+}
+
+/*
+** Return TRUE if an UPDATE or DELETE statement can operate directly on
+** the rowids returned by a WHERE clause.  Return FALSE if doing an
+** UPDATE or DELETE might change subsequent WHERE clause results.
+**
+** If the ONEPASS optimization is used (if this routine returns true)
+** then also write the indices of open cursors used by ONEPASS
+** into aiCur[0] and aiCur[1].  iaCur[0] gets the cursor of the data
+** table and iaCur[1] gets the cursor used by an auxiliary index.
+** Either value may be -1, indicating that cursor is not used.
+** Any cursors returned will have been opened for writing.
+**
+** aiCur[0] and aiCur[1] both get -1 if the where-clause logic is
+** unable to use the ONEPASS optimization.
+*/
+int sqlite3WhereOkOnePass(WhereInfo *pWInfo, int *aiCur){
+  memcpy(aiCur, pWInfo->aiCurOnePass, sizeof(int)*2);
+  return pWInfo->okOnePass;
+}
+
+/*
+** Move the content of pSrc into pDest
+*/
+static void whereOrMove(WhereOrSet *pDest, WhereOrSet *pSrc){
+  pDest->n = pSrc->n;
+  memcpy(pDest->a, pSrc->a, pDest->n*sizeof(pDest->a[0]));
+}
+
+/*
+** Try to insert a new prerequisite/cost entry into the WhereOrSet pSet.
+**
+** The new entry might overwrite an existing entry, or it might be
+** appended, or it might be discarded.  Do whatever is the right thing
+** so that pSet keeps the N_OR_COST best entries seen so far.
+*/
+static int whereOrInsert(
+  WhereOrSet *pSet,      /* The WhereOrSet to be updated */
+  Bitmask prereq,        /* Prerequisites of the new entry */
+  LogEst rRun,           /* Run-cost of the new entry */
+  LogEst nOut            /* Number of outputs for the new entry */
+){
+  u16 i;
+  WhereOrCost *p;
+  for(i=pSet->n, p=pSet->a; i>0; i--, p++){
+    if( rRun<=p->rRun && (prereq & p->prereq)==prereq ){
+      goto whereOrInsert_done;
+    }
+    if( p->rRun<=rRun && (p->prereq & prereq)==p->prereq ){
+      return 0;
+    }
+  }
+  if( pSet->n<N_OR_COST ){
+    p = &pSet->a[pSet->n++];
+    p->nOut = nOut;
+  }else{
+    p = pSet->a;
+    for(i=1; i<pSet->n; i++){
+      if( p->rRun>pSet->a[i].rRun ) p = pSet->a + i;
+    }
+    if( p->rRun<=rRun ) return 0;
+  }
+whereOrInsert_done:
+  p->prereq = prereq;
+  p->rRun = rRun;
+  if( p->nOut>nOut ) p->nOut = nOut;
+  return 1;
+}
+
+/*
+** Initialize a preallocated WhereClause structure.
+*/
+static void whereClauseInit(
+  WhereClause *pWC,        /* The WhereClause to be initialized */
+  WhereInfo *pWInfo        /* The WHERE processing context */
+){
+  pWC->pWInfo = pWInfo;
+  pWC->pOuter = 0;
+  pWC->nTerm = 0;
+  pWC->nSlot = ArraySize(pWC->aStatic);
+  pWC->a = pWC->aStatic;
+}
+
+/* Forward reference */
+static void whereClauseClear(WhereClause*);
+
+/*
+** Deallocate all memory associated with a WhereOrInfo object.
+*/
+static void whereOrInfoDelete(sqlite3 *db, WhereOrInfo *p){
+  whereClauseClear(&p->wc);
+  sqlite3DbFree(db, p);
+}
+
+/*
+** Deallocate all memory associated with a WhereAndInfo object.
+*/
+static void whereAndInfoDelete(sqlite3 *db, WhereAndInfo *p){
+  whereClauseClear(&p->wc);
+  sqlite3DbFree(db, p);
+}
+
+/*
+** Deallocate a WhereClause structure.  The WhereClause structure
+** itself is not freed.  This routine is the inverse of whereClauseInit().
+*/
+static void whereClauseClear(WhereClause *pWC){
+  int i;
+  WhereTerm *a;
+  sqlite3 *db = pWC->pWInfo->pParse->db;
+  for(i=pWC->nTerm-1, a=pWC->a; i>=0; i--, a++){
+    if( a->wtFlags & TERM_DYNAMIC ){
+      sqlite3ExprDelete(db, a->pExpr);
+    }
+    if( a->wtFlags & TERM_ORINFO ){
+      whereOrInfoDelete(db, a->u.pOrInfo);
+    }else if( a->wtFlags & TERM_ANDINFO ){
+      whereAndInfoDelete(db, a->u.pAndInfo);
+    }
+  }
+  if( pWC->a!=pWC->aStatic ){
+    sqlite3DbFree(db, pWC->a);
+  }
+}
+
+/*
+** Add a single new WhereTerm entry to the WhereClause object pWC.
+** The new WhereTerm object is constructed from Expr p and with wtFlags.
+** The index in pWC->a[] of the new WhereTerm is returned on success.
+** 0 is returned if the new WhereTerm could not be added due to a memory
+** allocation error.  The memory allocation failure will be recorded in
+** the db->mallocFailed flag so that higher-level functions can detect it.
+**
+** This routine will increase the size of the pWC->a[] array as necessary.
+**
+** If the wtFlags argument includes TERM_DYNAMIC, then responsibility
+** for freeing the expression p is assumed by the WhereClause object pWC.
+** This is true even if this routine fails to allocate a new WhereTerm.
+**
+** WARNING:  This routine might reallocate the space used to store
+** WhereTerms.  All pointers to WhereTerms should be invalidated after
+** calling this routine.  Such pointers may be reinitialized by referencing
+** the pWC->a[] array.
+*/
+static int whereClauseInsert(WhereClause *pWC, Expr *p, u8 wtFlags){
+  WhereTerm *pTerm;
+  int idx;
+  testcase( wtFlags & TERM_VIRTUAL );
+  if( pWC->nTerm>=pWC->nSlot ){
+    WhereTerm *pOld = pWC->a;
+    sqlite3 *db = pWC->pWInfo->pParse->db;
+    pWC->a = sqlite3DbMallocRaw(db, sizeof(pWC->a[0])*pWC->nSlot*2 );
+    if( pWC->a==0 ){
+      if( wtFlags & TERM_DYNAMIC ){
+        sqlite3ExprDelete(db, p);
+      }
+      pWC->a = pOld;
+      return 0;
+    }
+    memcpy(pWC->a, pOld, sizeof(pWC->a[0])*pWC->nTerm);
+    if( pOld!=pWC->aStatic ){
+      sqlite3DbFree(db, pOld);
+    }
+    pWC->nSlot = sqlite3DbMallocSize(db, pWC->a)/sizeof(pWC->a[0]);
+  }
+  pTerm = &pWC->a[idx = pWC->nTerm++];
+  if( p && ExprHasProperty(p, EP_Unlikely) ){
+    pTerm->truthProb = sqlite3LogEst(p->iTable) - 99;
+  }else{
+    pTerm->truthProb = 1;
+  }
+  pTerm->pExpr = sqlite3ExprSkipCollate(p);
+  pTerm->wtFlags = wtFlags;
+  pTerm->pWC = pWC;
+  pTerm->iParent = -1;
+  return idx;
+}
+
+/*
+** This routine identifies subexpressions in the WHERE clause where
+** each subexpression is separated by the AND operator or some other
+** operator specified in the op parameter.  The WhereClause structure
+** is filled with pointers to subexpressions.  For example:
+**
+**    WHERE  a=='hello' AND coalesce(b,11)<10 AND (c+12!=d OR c==22)
+**           \________/     \_______________/     \________________/
+**            slot[0]            slot[1]               slot[2]
+**
+** The original WHERE clause in pExpr is unaltered.  All this routine
+** does is make slot[] entries point to substructure within pExpr.
+**
+** In the previous sentence and in the diagram, "slot[]" refers to
+** the WhereClause.a[] array.  The slot[] array grows as needed to contain
+** all terms of the WHERE clause.
+*/
+static void whereSplit(WhereClause *pWC, Expr *pExpr, u8 op){
+  pWC->op = 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 a WhereMaskSet object
+*/
+#define initMaskSet(P)  (P)->n=0
+
+/*
+** Return the bitmask for the given cursor number.  Return 0 if
+** iCursor is not in the set.
+*/
+static Bitmask getMask(WhereMaskSet *pMaskSet, int iCursor){
+  int i;
+  assert( pMaskSet->n<=(int)sizeof(Bitmask)*8 );
+  for(i=0; i<pMaskSet->n; i++){
+    if( pMaskSet->ix[i]==iCursor ){
+      return MASKBIT(i);
+    }
+  }
+  return 0;
+}
+
+/*
+** Create a new mask for cursor iCursor.
+**
+** There is one cursor per table in the FROM clause.  The number of
+** tables in the FROM clause is limited by a test early in the
+** sqlite3WhereBegin() routine.  So we know that the pMaskSet->ix[]
+** array will never overflow.
+*/
+static void createMask(WhereMaskSet *pMaskSet, int iCursor){
+  assert( pMaskSet->n < ArraySize(pMaskSet->ix) );
+  pMaskSet->ix[pMaskSet->n++] = iCursor;
+}
+
+/*
+** These routines walk (recursively) an expression tree and generate
+** a bitmask indicating which tables are used in that expression
+** tree.
+*/
+static Bitmask exprListTableUsage(WhereMaskSet*, ExprList*);
+static Bitmask exprSelectTableUsage(WhereMaskSet*, Select*);
+static Bitmask exprTableUsage(WhereMaskSet *pMaskSet, Expr *p){
+  Bitmask mask = 0;
+  if( p==0 ) return 0;
+  if( p->op==TK_COLUMN ){
+    mask = getMask(pMaskSet, p->iTable);
+    return mask;
+  }
+  mask = exprTableUsage(pMaskSet, p->pRight);
+  mask |= exprTableUsage(pMaskSet, p->pLeft);
+  if( ExprHasProperty(p, EP_xIsSelect) ){
+    mask |= exprSelectTableUsage(pMaskSet, p->x.pSelect);
+  }else{
+    mask |= exprListTableUsage(pMaskSet, p->x.pList);
+  }
+  return mask;
+}
+static Bitmask exprListTableUsage(WhereMaskSet *pMaskSet, ExprList *pList){
+  int i;
+  Bitmask mask = 0;
+  if( pList ){
+    for(i=0; i<pList->nExpr; i++){
+      mask |= exprTableUsage(pMaskSet, pList->a[i].pExpr);
+    }
+  }
+  return mask;
+}
+static Bitmask exprSelectTableUsage(WhereMaskSet *pMaskSet, Select *pS){
+  Bitmask mask = 0;
+  while( pS ){
+    SrcList *pSrc = pS->pSrc;
+    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);
+    if( ALWAYS(pSrc!=0) ){
+      int i;
+      for(i=0; i<pSrc->nSrc; i++){
+        mask |= exprSelectTableUsage(pMaskSet, pSrc->a[i].pSelect);
+        mask |= exprTableUsage(pMaskSet, pSrc->a[i].pOn);
+      }
+    }
+    pS = pS->pPrior;
+  }
+  return mask;
+}
+
+/*
+** Return TRUE if the given operator is one of the operators that is
+** allowed for an indexable WHERE clause term.  The allowed operators are
+** "=", "<", ">", "<=", ">=", "IN", and "IS NULL"
+*/
+static int allowedOp(int op){
+  assert( TK_GT>TK_EQ && TK_GT<TK_GE );
+  assert( TK_LT>TK_EQ && TK_LT<TK_GE );
+  assert( TK_LE>TK_EQ && TK_LE<TK_GE );
+  assert( TK_GE==TK_EQ+4 );
+  return op==TK_IN || (op>=TK_EQ && op<=TK_GE) || op==TK_ISNULL;
+}
+
+/*
+** Commute a comparison operator.  Expressions of the form "X op Y"
+** are converted into "Y op X".
+**
+** If left/right precedence rules come into play when determining the
+** collating sequence, then COLLATE operators are adjusted to ensure
+** that the collating sequence does not change.  For example:
+** "Y collate NOCASE op X" becomes "X op Y" because any collation sequence on
+** the left hand side of a comparison overrides any collation sequence 
+** attached to the right. For the same reason the EP_Collate flag
+** is not commuted.
+*/
+static void exprCommute(Parse *pParse, Expr *pExpr){
+  u16 expRight = (pExpr->pRight->flags & EP_Collate);
+  u16 expLeft = (pExpr->pLeft->flags & EP_Collate);
+  assert( allowedOp(pExpr->op) && pExpr->op!=TK_IN );
+  if( expRight==expLeft ){
+    /* Either X and Y both have COLLATE operator or neither do */
+    if( expRight ){
+      /* Both X and Y have COLLATE operators.  Make sure X is always
+      ** used by clearing the EP_Collate flag from Y. */
+      pExpr->pRight->flags &= ~EP_Collate;
+    }else if( sqlite3ExprCollSeq(pParse, pExpr->pLeft)!=0 ){
+      /* Neither X nor Y have COLLATE operators, but X has a non-default
+      ** collating sequence.  So add the EP_Collate marker on X to cause
+      ** it to be searched first. */
+      pExpr->pLeft->flags |= EP_Collate;
+    }
+  }
+  SWAP(Expr*,pExpr->pRight,pExpr->pLeft);
+  if( pExpr->op>=TK_GT ){
+    assert( TK_LT==TK_GT+2 );
+    assert( TK_GE==TK_LE+2 );
+    assert( TK_GT>TK_EQ );
+    assert( TK_GT<TK_LE );
+    assert( pExpr->op>=TK_GT && pExpr->op<=TK_GE );
+    pExpr->op = ((pExpr->op-TK_GT)^2)+TK_GT;
+  }
+}
+
+/*
+** Translate from TK_xx operator to WO_xx bitmask.
+*/
+static u16 operatorMask(int op){
+  u16 c;
+  assert( allowedOp(op) );
+  if( op==TK_IN ){
+    c = WO_IN;
+  }else if( op==TK_ISNULL ){
+    c = WO_ISNULL;
+  }else{
+    assert( (WO_EQ<<(op-TK_EQ)) < 0x7fff );
+    c = (u16)(WO_EQ<<(op-TK_EQ));
+  }
+  assert( op!=TK_ISNULL || c==WO_ISNULL );
+  assert( op!=TK_IN || c==WO_IN );
+  assert( op!=TK_EQ || c==WO_EQ );
+  assert( op!=TK_LT || c==WO_LT );
+  assert( op!=TK_LE || c==WO_LE );
+  assert( op!=TK_GT || c==WO_GT );
+  assert( op!=TK_GE || c==WO_GE );
+  return c;
+}
+
+/*
+** Advance to the next WhereTerm that matches according to the criteria
+** established when the pScan object was initialized by whereScanInit().
+** Return NULL if there are no more matching WhereTerms.
+*/
+static WhereTerm *whereScanNext(WhereScan *pScan){
+  int iCur;            /* The cursor on the LHS of the term */
+  int iColumn;         /* The column on the LHS of the term.  -1 for IPK */
+  Expr *pX;            /* An expression being tested */
+  WhereClause *pWC;    /* Shorthand for pScan->pWC */
+  WhereTerm *pTerm;    /* The term being tested */
+  int k = pScan->k;    /* Where to start scanning */
+
+  while( pScan->iEquiv<=pScan->nEquiv ){
+    iCur = pScan->aEquiv[pScan->iEquiv-2];
+    iColumn = pScan->aEquiv[pScan->iEquiv-1];
+    while( (pWC = pScan->pWC)!=0 ){
+      for(pTerm=pWC->a+k; k<pWC->nTerm; k++, pTerm++){
+        if( pTerm->leftCursor==iCur
+         && pTerm->u.leftColumn==iColumn
+         && (pScan->iEquiv<=2 || !ExprHasProperty(pTerm->pExpr, EP_FromJoin))
+        ){
+          if( (pTerm->eOperator & WO_EQUIV)!=0
+           && pScan->nEquiv<ArraySize(pScan->aEquiv)
+          ){
+            int j;
+            pX = sqlite3ExprSkipCollate(pTerm->pExpr->pRight);
+            assert( pX->op==TK_COLUMN );
+            for(j=0; j<pScan->nEquiv; j+=2){
+              if( pScan->aEquiv[j]==pX->iTable
+               && pScan->aEquiv[j+1]==pX->iColumn ){
+                  break;
+              }
+            }
+            if( j==pScan->nEquiv ){
+              pScan->aEquiv[j] = pX->iTable;
+              pScan->aEquiv[j+1] = pX->iColumn;
+              pScan->nEquiv += 2;
+            }
+          }
+          if( (pTerm->eOperator & pScan->opMask)!=0 ){
+            /* Verify the affinity and collating sequence match */
+            if( pScan->zCollName && (pTerm->eOperator & WO_ISNULL)==0 ){
+              CollSeq *pColl;
+              Parse *pParse = pWC->pWInfo->pParse;
+              pX = pTerm->pExpr;
+              if( !sqlite3IndexAffinityOk(pX, pScan->idxaff) ){
+                continue;
+              }
+              assert(pX->pLeft);
+              pColl = sqlite3BinaryCompareCollSeq(pParse,
+                                                  pX->pLeft, pX->pRight);
+              if( pColl==0 ) pColl = pParse->db->pDfltColl;
+              if( sqlite3StrICmp(pColl->zName, pScan->zCollName) ){
+                continue;
+              }
+            }
+            if( (pTerm->eOperator & WO_EQ)!=0
+             && (pX = pTerm->pExpr->pRight)->op==TK_COLUMN
+             && pX->iTable==pScan->aEquiv[0]
+             && pX->iColumn==pScan->aEquiv[1]
+            ){
+              continue;
+            }
+            pScan->k = k+1;
+            return pTerm;
+          }
+        }
+      }
+      pScan->pWC = pScan->pWC->pOuter;
+      k = 0;
+    }
+    pScan->pWC = pScan->pOrigWC;
+    k = 0;
+    pScan->iEquiv += 2;
+  }
+  return 0;
+}
+
+/*
+** Initialize a WHERE clause scanner object.  Return a pointer to the
+** first match.  Return NULL if there are no matches.
+**
+** The scanner will be searching the WHERE clause pWC.  It will look
+** for terms of the form "X <op> <expr>" where X is column iColumn of table
+** iCur.  The <op> must be one of the operators described by opMask.
+**
+** If the search is for X and the WHERE clause contains terms of the
+** form X=Y then this routine might also return terms of the form
+** "Y <op> <expr>".  The number of levels of transitivity is limited,
+** but is enough to handle most commonly occurring SQL statements.
+**
+** If X is not the INTEGER PRIMARY KEY then X must be compatible with
+** index pIdx.
+*/
+static WhereTerm *whereScanInit(
+  WhereScan *pScan,       /* The WhereScan object being initialized */
+  WhereClause *pWC,       /* The WHERE clause to be scanned */
+  int iCur,               /* Cursor to scan for */
+  int iColumn,            /* Column to scan for */
+  u32 opMask,             /* Operator(s) to scan for */
+  Index *pIdx             /* Must be compatible with this index */
+){
+  int j;
+
+  /* memset(pScan, 0, sizeof(*pScan)); */
+  pScan->pOrigWC = pWC;
+  pScan->pWC = pWC;
+  if( pIdx && iColumn>=0 ){
+    pScan->idxaff = pIdx->pTable->aCol[iColumn].affinity;
+    for(j=0; pIdx->aiColumn[j]!=iColumn; j++){
+      if( NEVER(j>pIdx->nColumn) ) return 0;
+    }
+    pScan->zCollName = pIdx->azColl[j];
+  }else{
+    pScan->idxaff = 0;
+    pScan->zCollName = 0;
+  }
+  pScan->opMask = opMask;
+  pScan->k = 0;
+  pScan->aEquiv[0] = iCur;
+  pScan->aEquiv[1] = iColumn;
+  pScan->nEquiv = 2;
+  pScan->iEquiv = 2;
+  return whereScanNext(pScan);
+}
+
+/*
+** 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.
+**
+** The term returned might by Y=<expr> if there is another constraint in
+** the WHERE clause that specifies that X=Y.  Any such constraints will be
+** identified by the WO_EQUIV bit in the pTerm->eOperator field.  The
+** aEquiv[] array holds X and all its equivalents, with each SQL variable
+** taking up two slots in aEquiv[].  The first slot is for the cursor number
+** and the second is for the column number.  There are 22 slots in aEquiv[]
+** so that means we can look for X plus up to 10 other equivalent values.
+** Hence a search for X will return <expr> if X=A1 and A1=A2 and A2=A3
+** and ... and A9=A10 and A10=<expr>.
+**
+** If there are multiple terms in the WHERE clause of the form "X <op> <expr>"
+** then try for the one with no dependencies on <expr> - in other words where
+** <expr> is a constant expression of some kind.  Only return entries of
+** the form "X <op> Y" where Y is a column in another table if no terms of
+** the form "X <op> <const-expr>" exist.   If no terms with a constant RHS
+** exist, try to return a term that does not use WO_EQUIV.
+*/
+static WhereTerm *findTerm(
+  WhereClause *pWC,     /* The WHERE clause to be searched */
+  int iCur,             /* Cursor number of LHS */
+  int iColumn,          /* Column number of LHS */
+  Bitmask notReady,     /* RHS must not overlap with this mask */
+  u32 op,               /* Mask of WO_xx values describing operator */
+  Index *pIdx           /* Must be compatible with this index, if not NULL */
+){
+  WhereTerm *pResult = 0;
+  WhereTerm *p;
+  WhereScan scan;
+
+  p = whereScanInit(&scan, pWC, iCur, iColumn, op, pIdx);
+  while( p ){
+    if( (p->prereqRight & notReady)==0 ){
+      if( p->prereqRight==0 && (p->eOperator&WO_EQ)!=0 ){
+        return p;
+      }
+      if( pResult==0 ) pResult = p;
+    }
+    p = whereScanNext(&scan);
+  }
+  return pResult;
+}
+
+/* Forward reference */
+static void exprAnalyze(SrcList*, WhereClause*, int);
+
+/*
+** Call exprAnalyze on all terms in a WHERE clause.  
+*/
+static void exprAnalyzeAll(
+  SrcList *pTabList,       /* the FROM clause */
+  WhereClause *pWC         /* the WHERE clause to be analyzed */
+){
+  int i;
+  for(i=pWC->nTerm-1; i>=0; i--){
+    exprAnalyze(pTabList, pWC, i);
+  }
+}
+
+#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION
+/*
+** Check to see if the given expression is a LIKE or GLOB operator that
+** can be optimized using inequality constraints.  Return TRUE if it is
+** so and false if not.
+**
+** In order for the operator to be optimizible, the RHS must be a string
+** literal that does not begin with a wildcard.  
+*/
+static int isLikeOrGlob(
+  Parse *pParse,    /* Parsing and code generating context */
+  Expr *pExpr,      /* Test this expression */
+  Expr **ppPrefix,  /* Pointer to TK_STRING expression with pattern prefix */
+  int *pisComplete, /* True if the only wildcard is % in the last character */
+  int *pnoCase      /* True if uppercase is equivalent to lowercase */
+){
+  const char *z = 0;         /* String on RHS of LIKE operator */
+  Expr *pRight, *pLeft;      /* Right and left size of LIKE operator */
+  ExprList *pList;           /* List of operands to the LIKE operator */
+  int c;                     /* One character in z[] */
+  int cnt;                   /* Number of non-wildcard prefix characters */
+  char wc[3];                /* Wildcard characters */
+  sqlite3 *db = pParse->db;  /* Database connection */
+  sqlite3_value *pVal = 0;
+  int op;                    /* Opcode of pRight */
+
+  if( !sqlite3IsLikeFunction(db, pExpr, pnoCase, wc) ){
+    return 0;
+  }
+#ifdef SQLITE_EBCDIC
+  if( *pnoCase ) return 0;
+#endif
+  pList = pExpr->x.pList;
+  pLeft = pList->a[1].pExpr;
+  if( pLeft->op!=TK_COLUMN 
+   || sqlite3ExprAffinity(pLeft)!=SQLITE_AFF_TEXT 
+   || IsVirtual(pLeft->pTab)
+  ){
+    /* IMP: R-02065-49465 The left-hand side of the LIKE or GLOB operator must
+    ** be the name of an indexed column with TEXT affinity. */
+    return 0;
+  }
+  assert( pLeft->iColumn!=(-1) ); /* Because IPK never has AFF_TEXT */
+
+  pRight = sqlite3ExprSkipCollate(pList->a[0].pExpr);
+  op = pRight->op;
+  if( op==TK_VARIABLE ){
+    Vdbe *pReprepare = pParse->pReprepare;
+    int iCol = pRight->iColumn;
+    pVal = sqlite3VdbeGetBoundValue(pReprepare, iCol, SQLITE_AFF_NONE);
+    if( pVal && sqlite3_value_type(pVal)==SQLITE_TEXT ){
+      z = (char *)sqlite3_value_text(pVal);
+    }
+    sqlite3VdbeSetVarmask(pParse->pVdbe, iCol);
+    assert( pRight->op==TK_VARIABLE || pRight->op==TK_REGISTER );
+  }else if( op==TK_STRING ){
+    z = pRight->u.zToken;
+  }
+  if( z ){
+    cnt = 0;
+    while( (c=z[cnt])!=0 && c!=wc[0] && c!=wc[1] && c!=wc[2] ){
+      cnt++;
+    }
+    if( cnt!=0 && 255!=(u8)z[cnt-1] ){
+      Expr *pPrefix;
+      *pisComplete = c==wc[0] && z[cnt+1]==0;
+      pPrefix = sqlite3Expr(db, TK_STRING, z);
+      if( pPrefix ) pPrefix->u.zToken[cnt] = 0;
+      *ppPrefix = pPrefix;
+      if( op==TK_VARIABLE ){
+        Vdbe *v = pParse->pVdbe;
+        sqlite3VdbeSetVarmask(v, pRight->iColumn);
+        if( *pisComplete && pRight->u.zToken[1] ){
+          /* If the rhs of the LIKE expression is a variable, and the current
+          ** value of the variable means there is no need to invoke the LIKE
+          ** function, then no OP_Variable will be added to the program.
+          ** This causes problems for the sqlite3_bind_parameter_name()
+          ** API. To work around them, add a dummy OP_Variable here.
+          */ 
+          int r1 = sqlite3GetTempReg(pParse);
+          sqlite3ExprCodeTarget(pParse, pRight, r1);
+          sqlite3VdbeChangeP3(v, sqlite3VdbeCurrentAddr(v)-1, 0);
+          sqlite3ReleaseTempReg(pParse, r1);
+        }
+      }
+    }else{
+      z = 0;
+    }
+  }
+
+  sqlite3ValueFree(pVal);
+  return (z!=0);
+}
+#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */
+
+
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+/*
+** Check to see if the given expression is of the form
+**
+**         column MATCH expr
+**
+** If it is then return TRUE.  If not, return FALSE.
+*/
+static int isMatchOfColumn(
+  Expr *pExpr      /* Test this expression */
+){
+  ExprList *pList;
+
+  if( pExpr->op!=TK_FUNCTION ){
+    return 0;
+  }
+  if( sqlite3StrICmp(pExpr->u.zToken,"match")!=0 ){
+    return 0;
+  }
+  pList = pExpr->x.pList;
+  if( pList->nExpr!=2 ){
+    return 0;
+  }
+  if( pList->a[1].pExpr->op != TK_COLUMN ){
+    return 0;
+  }
+  return 1;
+}
+#endif /* SQLITE_OMIT_VIRTUALTABLE */
+
+/*
+** If the pBase expression originated in the ON or USING clause of
+** a join, then transfer the appropriate markings over to derived.
+*/
+static void transferJoinMarkings(Expr *pDerived, Expr *pBase){
+  if( pDerived ){
+    pDerived->flags |= pBase->flags & EP_FromJoin;
+    pDerived->iRightJoinTable = pBase->iRightJoinTable;
+  }
+}
+
+#if !defined(SQLITE_OMIT_OR_OPTIMIZATION) && !defined(SQLITE_OMIT_SUBQUERY)
+/*
+** Analyze a term that consists of two or more OR-connected
+** subterms.  So in:
+**
+**     ... WHERE  (a=5) AND (b=7 OR c=9 OR d=13) AND (d=13)
+**                          ^^^^^^^^^^^^^^^^^^^^
+**
+** This routine analyzes terms such as the middle term in the above example.
+** A WhereOrTerm object is computed and attached to the term under
+** analysis, regardless of the outcome of the analysis.  Hence:
+**
+**     WhereTerm.wtFlags   |=  TERM_ORINFO
+**     WhereTerm.u.pOrInfo  =  a dynamically allocated WhereOrTerm object
+**
+** The term being analyzed must have two or more of OR-connected subterms.
+** A single subterm might be a set of AND-connected sub-subterms.
+** Examples of terms under analysis:
+**
+**     (A)     t1.x=t2.y OR t1.x=t2.z OR t1.y=15 OR t1.z=t3.a+5
+**     (B)     x=expr1 OR expr2=x OR x=expr3
+**     (C)     t1.x=t2.y OR (t1.x=t2.z AND t1.y=15)
+**     (D)     x=expr1 OR (y>11 AND y<22 AND z LIKE '*hello*')
+**     (E)     (p.a=1 AND q.b=2 AND r.c=3) OR (p.x=4 AND q.y=5 AND r.z=6)
+**
+** CASE 1:
+**
+** If all subterms are of the form T.C=expr for some single column of C and
+** a single table T (as shown in example B above) then create a new virtual
+** term that is an equivalent IN expression.  In other words, if the term
+** being analyzed is:
+**
+**      x = expr1  OR  expr2 = x  OR  x = expr3
+**
+** then create a new virtual term like this:
+**
+**      x IN (expr1,expr2,expr3)
+**
+** CASE 2:
+**
+** If all subterms are indexable by a single table T, then set
+**
+**     WhereTerm.eOperator              =  WO_OR
+**     WhereTerm.u.pOrInfo->indexable  |=  the cursor number for table T
+**
+** A subterm is "indexable" if it is of the form
+** "T.C <op> <expr>" where C is any column of table T and 
+** <op> is one of "=", "<", "<=", ">", ">=", "IS NULL", or "IN".
+** A subterm is also indexable if it is an AND of two or more
+** subsubterms at least one of which is indexable.  Indexable AND 
+** subterms have their eOperator set to WO_AND and they have
+** u.pAndInfo set to a dynamically allocated WhereAndTerm object.
+**
+** From another point of view, "indexable" means that the subterm could
+** potentially be used with an index if an appropriate index exists.
+** This analysis does not consider whether or not the index exists; that
+** is decided elsewhere.  This analysis only looks at whether subterms
+** appropriate for indexing exist.
+**
+** All examples A through E above satisfy case 2.  But if a term
+** also satisfies case 1 (such as B) we know that the optimizer will
+** always prefer case 1, so in that case we pretend that case 2 is not
+** satisfied.
+**
+** It might be the case that multiple tables are indexable.  For example,
+** (E) above is indexable on tables P, Q, and R.
+**
+** Terms that satisfy case 2 are candidates for lookup by using
+** separate indices to find rowids for each subterm and composing
+** the union of all rowids using a RowSet object.  This is similar
+** to "bitmap indices" in other database engines.
+**
+** OTHERWISE:
+**
+** If neither case 1 nor case 2 apply, then leave the eOperator set to
+** zero.  This term is not useful for search.
+*/
+static void exprAnalyzeOrTerm(
+  SrcList *pSrc,            /* the FROM clause */
+  WhereClause *pWC,         /* the complete WHERE clause */
+  int idxTerm               /* Index of the OR-term to be analyzed */
+){
+  WhereInfo *pWInfo = pWC->pWInfo;        /* WHERE clause processing context */
+  Parse *pParse = pWInfo->pParse;         /* Parser context */
+  sqlite3 *db = pParse->db;               /* Database connection */
+  WhereTerm *pTerm = &pWC->a[idxTerm];    /* The term to be analyzed */
+  Expr *pExpr = pTerm->pExpr;             /* The expression of the term */
+  int i;                                  /* Loop counters */
+  WhereClause *pOrWc;       /* Breakup of pTerm into subterms */
+  WhereTerm *pOrTerm;       /* A Sub-term within the pOrWc */
+  WhereOrInfo *pOrInfo;     /* Additional information associated with pTerm */
+  Bitmask chngToIN;         /* Tables that might satisfy case 1 */
+  Bitmask indexable;        /* Tables that are indexable, satisfying case 2 */
+
+  /*
+  ** Break the OR clause into its separate subterms.  The subterms are
+  ** stored in a WhereClause structure containing within the WhereOrInfo
+  ** object that is attached to the original OR clause term.
+  */
+  assert( (pTerm->wtFlags & (TERM_DYNAMIC|TERM_ORINFO|TERM_ANDINFO))==0 );
+  assert( pExpr->op==TK_OR );
+  pTerm->u.pOrInfo = pOrInfo = sqlite3DbMallocZero(db, sizeof(*pOrInfo));
+  if( pOrInfo==0 ) return;
+  pTerm->wtFlags |= TERM_ORINFO;
+  pOrWc = &pOrInfo->wc;
+  whereClauseInit(pOrWc, pWInfo);
+  whereSplit(pOrWc, pExpr, TK_OR);
+  exprAnalyzeAll(pSrc, pOrWc);
+  if( db->mallocFailed ) return;
+  assert( pOrWc->nTerm>=2 );
+
+  /*
+  ** Compute the set of tables that might satisfy cases 1 or 2.
+  */
+  indexable = ~(Bitmask)0;
+  chngToIN = ~(Bitmask)0;
+  for(i=pOrWc->nTerm-1, pOrTerm=pOrWc->a; i>=0 && indexable; i--, pOrTerm++){
+    if( (pOrTerm->eOperator & WO_SINGLE)==0 ){
+      WhereAndInfo *pAndInfo;
+      assert( (pOrTerm->wtFlags & (TERM_ANDINFO|TERM_ORINFO))==0 );
+      chngToIN = 0;
+      pAndInfo = sqlite3DbMallocRaw(db, sizeof(*pAndInfo));
+      if( pAndInfo ){
+        WhereClause *pAndWC;
+        WhereTerm *pAndTerm;
+        int j;
+        Bitmask b = 0;
+        pOrTerm->u.pAndInfo = pAndInfo;
+        pOrTerm->wtFlags |= TERM_ANDINFO;
+        pOrTerm->eOperator = WO_AND;
+        pAndWC = &pAndInfo->wc;
+        whereClauseInit(pAndWC, pWC->pWInfo);
+        whereSplit(pAndWC, pOrTerm->pExpr, TK_AND);
+        exprAnalyzeAll(pSrc, pAndWC);
+        pAndWC->pOuter = pWC;
+        testcase( db->mallocFailed );
+        if( !db->mallocFailed ){
+          for(j=0, pAndTerm=pAndWC->a; j<pAndWC->nTerm; j++, pAndTerm++){
+            assert( pAndTerm->pExpr );
+            if( allowedOp(pAndTerm->pExpr->op) ){
+              b |= getMask(&pWInfo->sMaskSet, pAndTerm->leftCursor);
+            }
+          }
+        }
+        indexable &= b;
+      }
+    }else if( pOrTerm->wtFlags & TERM_COPIED ){
+      /* Skip this term for now.  We revisit it when we process the
+      ** corresponding TERM_VIRTUAL term */
+    }else{
+      Bitmask b;
+      b = getMask(&pWInfo->sMaskSet, pOrTerm->leftCursor);
+      if( pOrTerm->wtFlags & TERM_VIRTUAL ){
+        WhereTerm *pOther = &pOrWc->a[pOrTerm->iParent];
+        b |= getMask(&pWInfo->sMaskSet, pOther->leftCursor);
+      }
+      indexable &= b;
+      if( (pOrTerm->eOperator & WO_EQ)==0 ){
+        chngToIN = 0;
+      }else{
+        chngToIN &= b;
+      }
+    }
+  }
+
+  /*
+  ** Record the set of tables that satisfy case 2.  The set might be
+  ** empty.
+  */
+  pOrInfo->indexable = indexable;
+  pTerm->eOperator = indexable==0 ? 0 : WO_OR;
+
+  /*
+  ** chngToIN holds a set of tables that *might* satisfy case 1.  But
+  ** we have to do some additional checking to see if case 1 really
+  ** is satisfied.
+  **
+  ** chngToIN will hold either 0, 1, or 2 bits.  The 0-bit case means
+  ** that there is no possibility of transforming the OR clause into an
+  ** IN operator because one or more terms in the OR clause contain
+  ** something other than == on a column in the single table.  The 1-bit
+  ** case means that every term of the OR clause is of the form
+  ** "table.column=expr" for some single table.  The one bit that is set
+  ** will correspond to the common table.  We still need to check to make
+  ** sure the same column is used on all terms.  The 2-bit case is when
+  ** the all terms are of the form "table1.column=table2.column".  It
+  ** might be possible to form an IN operator with either table1.column
+  ** or table2.column as the LHS if either is common to every term of
+  ** the OR clause.
+  **
+  ** Note that terms of the form "table.column1=table.column2" (the
+  ** same table on both sizes of the ==) cannot be optimized.
+  */
+  if( chngToIN ){
+    int okToChngToIN = 0;     /* True if the conversion to IN is valid */
+    int iColumn = -1;         /* Column index on lhs of IN operator */
+    int iCursor = -1;         /* Table cursor common to all terms */
+    int j = 0;                /* Loop counter */
+
+    /* Search for a table and column that appears on one side or the
+    ** other of the == operator in every subterm.  That table and column
+    ** will be recorded in iCursor and iColumn.  There might not be any
+    ** such table and column.  Set okToChngToIN if an appropriate table
+    ** and column is found but leave okToChngToIN false if not found.
+    */
+    for(j=0; j<2 && !okToChngToIN; j++){
+      pOrTerm = pOrWc->a;
+      for(i=pOrWc->nTerm-1; i>=0; i--, pOrTerm++){
+        assert( pOrTerm->eOperator & WO_EQ );
+        pOrTerm->wtFlags &= ~TERM_OR_OK;
+        if( pOrTerm->leftCursor==iCursor ){
+          /* This is the 2-bit case and we are on the second iteration and
+          ** current term is from the first iteration.  So skip this term. */
+          assert( j==1 );
+          continue;
+        }
+        if( (chngToIN & getMask(&pWInfo->sMaskSet, pOrTerm->leftCursor))==0 ){
+          /* This term must be of the form t1.a==t2.b where t2 is in the
+          ** chngToIN set but t1 is not.  This term will be either preceded
+          ** or follwed by an inverted copy (t2.b==t1.a).  Skip this term 
+          ** and use its inversion. */
+          testcase( pOrTerm->wtFlags & TERM_COPIED );
+          testcase( pOrTerm->wtFlags & TERM_VIRTUAL );
+          assert( pOrTerm->wtFlags & (TERM_COPIED|TERM_VIRTUAL) );
+          continue;
+        }
+        iColumn = pOrTerm->u.leftColumn;
+        iCursor = pOrTerm->leftCursor;
+        break;
+      }
+      if( i<0 ){
+        /* No candidate table+column was found.  This can only occur
+        ** on the second iteration */
+        assert( j==1 );
+        assert( IsPowerOfTwo(chngToIN) );
+        assert( chngToIN==getMask(&pWInfo->sMaskSet, iCursor) );
+        break;
+      }
+      testcase( j==1 );
+
+      /* We have found a candidate table and column.  Check to see if that
+      ** table and column is common to every term in the OR clause */
+      okToChngToIN = 1;
+      for(; i>=0 && okToChngToIN; i--, pOrTerm++){
+        assert( pOrTerm->eOperator & WO_EQ );
+        if( pOrTerm->leftCursor!=iCursor ){
+          pOrTerm->wtFlags &= ~TERM_OR_OK;
+        }else if( pOrTerm->u.leftColumn!=iColumn ){
+          okToChngToIN = 0;
+        }else{
+          int affLeft, affRight;
+          /* If the right-hand side is also a column, then the affinities
+          ** of both right and left sides must be such that no type
+          ** conversions are required on the right.  (Ticket #2249)
+          */
+          affRight = sqlite3ExprAffinity(pOrTerm->pExpr->pRight);
+          affLeft = sqlite3ExprAffinity(pOrTerm->pExpr->pLeft);
+          if( affRight!=0 && affRight!=affLeft ){
+            okToChngToIN = 0;
+          }else{
+            pOrTerm->wtFlags |= TERM_OR_OK;
+          }
+        }
+      }
+    }
+
+    /* At this point, okToChngToIN is true if original pTerm satisfies
+    ** case 1.  In that case, construct a new virtual term that is 
+    ** pTerm converted into an IN operator.
+    */
+    if( okToChngToIN ){
+      Expr *pDup;            /* A transient duplicate expression */
+      ExprList *pList = 0;   /* The RHS of the IN operator */
+      Expr *pLeft = 0;       /* The LHS of the IN operator */
+      Expr *pNew;            /* The complete IN operator */
+
+      for(i=pOrWc->nTerm-1, pOrTerm=pOrWc->a; i>=0; i--, pOrTerm++){
+        if( (pOrTerm->wtFlags & TERM_OR_OK)==0 ) continue;
+        assert( pOrTerm->eOperator & WO_EQ );
+        assert( pOrTerm->leftCursor==iCursor );
+        assert( pOrTerm->u.leftColumn==iColumn );
+        pDup = sqlite3ExprDup(db, pOrTerm->pExpr->pRight, 0);
+        pList = sqlite3ExprListAppend(pWInfo->pParse, pList, pDup);
+        pLeft = pOrTerm->pExpr->pLeft;
+      }
+      assert( pLeft!=0 );
+      pDup = sqlite3ExprDup(db, pLeft, 0);
+      pNew = sqlite3PExpr(pParse, TK_IN, pDup, 0, 0);
+      if( pNew ){
+        int idxNew;
+        transferJoinMarkings(pNew, pExpr);
+        assert( !ExprHasProperty(pNew, EP_xIsSelect) );
+        pNew->x.pList = pList;
+        idxNew = whereClauseInsert(pWC, pNew, TERM_VIRTUAL|TERM_DYNAMIC);
+        testcase( idxNew==0 );
+        exprAnalyze(pSrc, pWC, idxNew);
+        pTerm = &pWC->a[idxTerm];
+        pWC->a[idxNew].iParent = idxTerm;
+        pTerm->nChild = 1;
+      }else{
+        sqlite3ExprListDelete(db, pList);
+      }
+      pTerm->eOperator = WO_NOOP;  /* case 1 trumps case 2 */
+    }
+  }
+}
+#endif /* !SQLITE_OMIT_OR_OPTIMIZATION && !SQLITE_OMIT_SUBQUERY */
+
+/*
+** The input to this routine is an WhereTerm structure with only the
+** "pExpr" field filled in.  The job of this routine is to analyze the
+** subexpression and populate all the other fields of the WhereTerm
+** structure.
+**
+** If the expression is of the form "<expr> <op> X" it gets commuted
+** to the standard form of "X <op> <expr>".
+**
+** If the expression is of the form "X <op> Y" where both X and Y are
+** columns, then the original expression is unchanged and a new virtual
+** term of the form "Y <op> X" is added to the WHERE clause and
+** analyzed separately.  The original term is marked with TERM_COPIED
+** and the new term is marked with TERM_DYNAMIC (because it's pExpr
+** needs to be freed with the WhereClause) and TERM_VIRTUAL (because it
+** is a commuted copy of a prior term.)  The original term has nChild=1
+** and the copy has idxParent set to the index of the original term.
+*/
+static void exprAnalyze(
+  SrcList *pSrc,            /* the FROM clause */
+  WhereClause *pWC,         /* the WHERE clause */
+  int idxTerm               /* Index of the term to be analyzed */
+){
+  WhereInfo *pWInfo = pWC->pWInfo; /* WHERE clause processing context */
+  WhereTerm *pTerm;                /* The term to be analyzed */
+  WhereMaskSet *pMaskSet;          /* Set of table index masks */
+  Expr *pExpr;                     /* The expression to be analyzed */
+  Bitmask prereqLeft;              /* Prerequesites of the pExpr->pLeft */
+  Bitmask prereqAll;               /* Prerequesites of pExpr */
+  Bitmask extraRight = 0;          /* Extra dependencies on LEFT JOIN */
+  Expr *pStr1 = 0;                 /* RHS of LIKE/GLOB operator */
+  int isComplete = 0;              /* RHS of LIKE/GLOB ends with wildcard */
+  int noCase = 0;                  /* LIKE/GLOB distinguishes case */
+  int op;                          /* Top-level operator.  pExpr->op */
+  Parse *pParse = pWInfo->pParse;  /* Parsing context */
+  sqlite3 *db = pParse->db;        /* Database connection */
+
+  if( db->mallocFailed ){
+    return;
+  }
+  pTerm = &pWC->a[idxTerm];
+  pMaskSet = &pWInfo->sMaskSet;
+  pExpr = pTerm->pExpr;
+  assert( pExpr->op!=TK_AS && pExpr->op!=TK_COLLATE );
+  prereqLeft = exprTableUsage(pMaskSet, pExpr->pLeft);
+  op = pExpr->op;
+  if( op==TK_IN ){
+    assert( pExpr->pRight==0 );
+    if( ExprHasProperty(pExpr, EP_xIsSelect) ){
+      pTerm->prereqRight = exprSelectTableUsage(pMaskSet, pExpr->x.pSelect);
+    }else{
+      pTerm->prereqRight = exprListTableUsage(pMaskSet, pExpr->x.pList);
+    }
+  }else if( op==TK_ISNULL ){
+    pTerm->prereqRight = 0;
+  }else{
+    pTerm->prereqRight = exprTableUsage(pMaskSet, pExpr->pRight);
+  }
+  prereqAll = exprTableUsage(pMaskSet, pExpr);
+  if( ExprHasProperty(pExpr, EP_FromJoin) ){
+    Bitmask x = getMask(pMaskSet, pExpr->iRightJoinTable);
+    prereqAll |= x;
+    extraRight = x-1;  /* ON clause terms may not be used with an index
+                       ** on left table of a LEFT JOIN.  Ticket #3015 */
+  }
+  pTerm->prereqAll = prereqAll;
+  pTerm->leftCursor = -1;
+  pTerm->iParent = -1;
+  pTerm->eOperator = 0;
+  if( allowedOp(op) ){
+    Expr *pLeft = sqlite3ExprSkipCollate(pExpr->pLeft);
+    Expr *pRight = sqlite3ExprSkipCollate(pExpr->pRight);
+    u16 opMask = (pTerm->prereqRight & prereqLeft)==0 ? WO_ALL : WO_EQUIV;
+    if( pLeft->op==TK_COLUMN ){
+      pTerm->leftCursor = pLeft->iTable;
+      pTerm->u.leftColumn = pLeft->iColumn;
+      pTerm->eOperator = operatorMask(op) & opMask;
+    }
+    if( pRight && pRight->op==TK_COLUMN ){
+      WhereTerm *pNew;
+      Expr *pDup;
+      u16 eExtraOp = 0;        /* Extra bits for pNew->eOperator */
+      if( pTerm->leftCursor>=0 ){
+        int idxNew;
+        pDup = sqlite3ExprDup(db, pExpr, 0);
+        if( db->mallocFailed ){
+          sqlite3ExprDelete(db, pDup);
+          return;
+        }
+        idxNew = whereClauseInsert(pWC, pDup, TERM_VIRTUAL|TERM_DYNAMIC);
+        if( idxNew==0 ) return;
+        pNew = &pWC->a[idxNew];
+        pNew->iParent = idxTerm;
+        pTerm = &pWC->a[idxTerm];
+        pTerm->nChild = 1;
+        pTerm->wtFlags |= TERM_COPIED;
+        if( pExpr->op==TK_EQ
+         && !ExprHasProperty(pExpr, EP_FromJoin)
+         && OptimizationEnabled(db, SQLITE_Transitive)
+        ){
+          pTerm->eOperator |= WO_EQUIV;
+          eExtraOp = WO_EQUIV;
+        }
+      }else{
+        pDup = pExpr;
+        pNew = pTerm;
+      }
+      exprCommute(pParse, pDup);
+      pLeft = sqlite3ExprSkipCollate(pDup->pLeft);
+      pNew->leftCursor = pLeft->iTable;
+      pNew->u.leftColumn = pLeft->iColumn;
+      testcase( (prereqLeft | extraRight) != prereqLeft );
+      pNew->prereqRight = prereqLeft | extraRight;
+      pNew->prereqAll = prereqAll;
+      pNew->eOperator = (operatorMask(pDup->op) + eExtraOp) & opMask;
+    }
+  }
+
+#ifndef SQLITE_OMIT_BETWEEN_OPTIMIZATION
+  /* If a term is the BETWEEN operator, create two new virtual terms
+  ** that define the range that the BETWEEN implements.  For example:
+  **
+  **      a BETWEEN b AND c
+  **
+  ** is converted into:
+  **
+  **      (a BETWEEN b AND c) AND (a>=b) AND (a<=c)
+  **
+  ** The two new terms are added onto the end of the WhereClause object.
+  ** The new terms are "dynamic" and are children of the original BETWEEN
+  ** term.  That means that if the BETWEEN term is coded, the children are
+  ** skipped.  Or, if the children are satisfied by an index, the original
+  ** BETWEEN term is skipped.
+  */
+  else if( pExpr->op==TK_BETWEEN && pWC->op==TK_AND ){
+    ExprList *pList = pExpr->x.pList;
+    int i;
+    static const u8 ops[] = {TK_GE, TK_LE};
+    assert( pList!=0 );
+    assert( pList->nExpr==2 );
+    for(i=0; i<2; i++){
+      Expr *pNewExpr;
+      int idxNew;
+      pNewExpr = sqlite3PExpr(pParse, ops[i], 
+                             sqlite3ExprDup(db, pExpr->pLeft, 0),
+                             sqlite3ExprDup(db, pList->a[i].pExpr, 0), 0);
+      transferJoinMarkings(pNewExpr, pExpr);
+      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);
+      testcase( idxNew==0 );
+      exprAnalyze(pSrc, pWC, idxNew);
+      pTerm = &pWC->a[idxTerm];
+      pWC->a[idxNew].iParent = idxTerm;
+    }
+    pTerm->nChild = 2;
+  }
+#endif /* SQLITE_OMIT_BETWEEN_OPTIMIZATION */
+
+#if !defined(SQLITE_OMIT_OR_OPTIMIZATION) && !defined(SQLITE_OMIT_SUBQUERY)
+  /* Analyze a term that is composed of two or more subterms connected by
+  ** an OR operator.
+  */
+  else if( pExpr->op==TK_OR ){
+    assert( pWC->op==TK_AND );
+    exprAnalyzeOrTerm(pSrc, pWC, idxTerm);
+    pTerm = &pWC->a[idxTerm];
+  }
+#endif /* SQLITE_OMIT_OR_OPTIMIZATION */
+
+#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION
+  /* Add constraints to reduce the search space on a LIKE or GLOB
+  ** operator.
+  **
+  ** A like pattern of the form "x LIKE 'abc%'" is changed into constraints
+  **
+  **          x>='abc' AND x<'abd' AND x LIKE 'abc%'
+  **
+  ** The last character of the prefix "abc" is incremented to form the
+  ** termination condition "abd".
+  */
+  if( pWC->op==TK_AND 
+   && isLikeOrGlob(pParse, pExpr, &pStr1, &isComplete, &noCase)
+  ){
+    Expr *pLeft;       /* LHS of LIKE/GLOB operator */
+    Expr *pStr2;       /* Copy of pStr1 - RHS of LIKE/GLOB operator */
+    Expr *pNewExpr1;
+    Expr *pNewExpr2;
+    int idxNew1;
+    int idxNew2;
+    Token sCollSeqName;  /* Name of collating sequence */
+
+    pLeft = pExpr->x.pList->a[1].pExpr;
+    pStr2 = sqlite3ExprDup(db, pStr1, 0);
+    if( !db->mallocFailed ){
+      u8 c, *pC;       /* Last character before the first wildcard */
+      pC = (u8*)&pStr2->u.zToken[sqlite3Strlen30(pStr2->u.zToken)-1];
+      c = *pC;
+      if( noCase ){
+        /* The point is to increment the last character before the first
+        ** wildcard.  But if we increment '@', that will push it into the
+        ** alphabetic range where case conversions will mess up the 
+        ** inequality.  To avoid this, make sure to also run the full
+        ** LIKE on all candidate expressions by clearing the isComplete flag
+        */
+        if( c=='A'-1 ) isComplete = 0;
+        c = sqlite3UpperToLower[c];
+      }
+      *pC = c + 1;
+    }
+    sCollSeqName.z = noCase ? "NOCASE" : "BINARY";
+    sCollSeqName.n = 6;
+    pNewExpr1 = sqlite3ExprDup(db, pLeft, 0);
+    pNewExpr1 = sqlite3PExpr(pParse, TK_GE, 
+           sqlite3ExprAddCollateToken(pParse,pNewExpr1,&sCollSeqName),
+           pStr1, 0);
+    transferJoinMarkings(pNewExpr1, pExpr);
+    idxNew1 = whereClauseInsert(pWC, pNewExpr1, TERM_VIRTUAL|TERM_DYNAMIC);
+    testcase( idxNew1==0 );
+    exprAnalyze(pSrc, pWC, idxNew1);
+    pNewExpr2 = sqlite3ExprDup(db, pLeft, 0);
+    pNewExpr2 = sqlite3PExpr(pParse, TK_LT,
+           sqlite3ExprAddCollateToken(pParse,pNewExpr2,&sCollSeqName),
+           pStr2, 0);
+    transferJoinMarkings(pNewExpr2, pExpr);
+    idxNew2 = whereClauseInsert(pWC, pNewExpr2, TERM_VIRTUAL|TERM_DYNAMIC);
+    testcase( idxNew2==0 );
+    exprAnalyze(pSrc, pWC, idxNew2);
+    pTerm = &pWC->a[idxTerm];
+    if( isComplete ){
+      pWC->a[idxNew1].iParent = idxTerm;
+      pWC->a[idxNew2].iParent = idxTerm;
+      pTerm->nChild = 2;
+    }
+  }
+#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */
+
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+  /* Add a WO_MATCH auxiliary term to the constraint set if the
+  ** current expression is of the form:  column MATCH expr.
+  ** This information is used by the xBestIndex methods of
+  ** virtual tables.  The native query optimizer does not attempt
+  ** to do anything with MATCH functions.
+  */
+  if( isMatchOfColumn(pExpr) ){
+    int idxNew;
+    Expr *pRight, *pLeft;
+    WhereTerm *pNewTerm;
+    Bitmask prereqColumn, prereqExpr;
+
+    pRight = pExpr->x.pList->a[0].pExpr;
+    pLeft = pExpr->x.pList->a[1].pExpr;
+    prereqExpr = exprTableUsage(pMaskSet, pRight);
+    prereqColumn = exprTableUsage(pMaskSet, pLeft);
+    if( (prereqExpr & prereqColumn)==0 ){
+      Expr *pNewExpr;
+      pNewExpr = sqlite3PExpr(pParse, TK_MATCH, 
+                              0, sqlite3ExprDup(db, pRight, 0), 0);
+      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);
+      testcase( idxNew==0 );
+      pNewTerm = &pWC->a[idxNew];
+      pNewTerm->prereqRight = prereqExpr;
+      pNewTerm->leftCursor = pLeft->iTable;
+      pNewTerm->u.leftColumn = pLeft->iColumn;
+      pNewTerm->eOperator = WO_MATCH;
+      pNewTerm->iParent = idxTerm;
+      pTerm = &pWC->a[idxTerm];
+      pTerm->nChild = 1;
+      pTerm->wtFlags |= TERM_COPIED;
+      pNewTerm->prereqAll = pTerm->prereqAll;
+    }
+  }
+#endif /* SQLITE_OMIT_VIRTUALTABLE */
+
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+  /* When sqlite_stat3 histogram data is available an operator of the
+  ** form "x IS NOT NULL" can sometimes be evaluated more efficiently
+  ** as "x>NULL" if x is not an INTEGER PRIMARY KEY.  So construct a
+  ** virtual term of that form.
+  **
+  ** Note that the virtual term must be tagged with TERM_VNULL.  This
+  ** TERM_VNULL tag will suppress the not-null check at the beginning
+  ** of the loop.  Without the TERM_VNULL flag, the not-null check at
+  ** the start of the loop will prevent any results from being returned.
+  */
+  if( pExpr->op==TK_NOTNULL
+   && pExpr->pLeft->op==TK_COLUMN
+   && pExpr->pLeft->iColumn>=0
+   && OptimizationEnabled(db, SQLITE_Stat3)
+  ){
+    Expr *pNewExpr;
+    Expr *pLeft = pExpr->pLeft;
+    int idxNew;
+    WhereTerm *pNewTerm;
+
+    pNewExpr = sqlite3PExpr(pParse, TK_GT,
+                            sqlite3ExprDup(db, pLeft, 0),
+                            sqlite3PExpr(pParse, TK_NULL, 0, 0, 0), 0);
+
+    idxNew = whereClauseInsert(pWC, pNewExpr,
+                              TERM_VIRTUAL|TERM_DYNAMIC|TERM_VNULL);
+    if( idxNew ){
+      pNewTerm = &pWC->a[idxNew];
+      pNewTerm->prereqRight = 0;
+      pNewTerm->leftCursor = pLeft->iTable;
+      pNewTerm->u.leftColumn = pLeft->iColumn;
+      pNewTerm->eOperator = WO_GT;
+      pNewTerm->iParent = idxTerm;
+      pTerm = &pWC->a[idxTerm];
+      pTerm->nChild = 1;
+      pTerm->wtFlags |= TERM_COPIED;
+      pNewTerm->prereqAll = pTerm->prereqAll;
+    }
+  }
+#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
+
+  /* Prevent ON clause terms of a LEFT JOIN from being used to drive
+  ** an index for tables to the left of the join.
+  */
+  pTerm->prereqRight |= extraRight;
+}
+
+/*
+** This function searches pList for an entry that matches the iCol-th column
+** of index pIdx.
+**
+** If such an expression is found, its index in pList->a[] is returned. If
+** no expression is found, -1 is returned.
+*/
+static int findIndexCol(
+  Parse *pParse,                  /* Parse context */
+  ExprList *pList,                /* Expression list to search */
+  int iBase,                      /* Cursor for table associated with pIdx */
+  Index *pIdx,                    /* Index to match column of */
+  int iCol                        /* Column of index to match */
+){
+  int i;
+  const char *zColl = pIdx->azColl[iCol];
+
+  for(i=0; i<pList->nExpr; i++){
+    Expr *p = sqlite3ExprSkipCollate(pList->a[i].pExpr);
+    if( p->op==TK_COLUMN
+     && p->iColumn==pIdx->aiColumn[iCol]
+     && p->iTable==iBase
+    ){
+      CollSeq *pColl = sqlite3ExprCollSeq(pParse, pList->a[i].pExpr);
+      if( ALWAYS(pColl) && 0==sqlite3StrICmp(pColl->zName, zColl) ){
+        return i;
+      }
+    }
+  }
+
+  return -1;
+}
+
+/*
+** Return true if the DISTINCT expression-list passed as the third argument
+** is redundant.
+**
+** A DISTINCT list is redundant if the database contains some subset of
+** columns that are unique and non-null.
+*/
+static int isDistinctRedundant(
+  Parse *pParse,            /* Parsing context */
+  SrcList *pTabList,        /* The FROM clause */
+  WhereClause *pWC,         /* The WHERE clause */
+  ExprList *pDistinct       /* The result set that needs to be DISTINCT */
+){
+  Table *pTab;
+  Index *pIdx;
+  int i;                          
+  int iBase;
+
+  /* If there is more than one table or sub-select in the FROM clause of
+  ** this query, then it will not be possible to show that the DISTINCT 
+  ** clause is redundant. */
+  if( pTabList->nSrc!=1 ) return 0;
+  iBase = pTabList->a[0].iCursor;
+  pTab = pTabList->a[0].pTab;
+
+  /* If any of the expressions is an IPK column on table iBase, then return 
+  ** true. Note: The (p->iTable==iBase) part of this test may be false if the
+  ** current SELECT is a correlated sub-query.
+  */
+  for(i=0; i<pDistinct->nExpr; i++){
+    Expr *p = sqlite3ExprSkipCollate(pDistinct->a[i].pExpr);
+    if( p->op==TK_COLUMN && p->iTable==iBase && p->iColumn<0 ) return 1;
+  }
+
+  /* Loop through all indices on the table, checking each to see if it makes
+  ** the DISTINCT qualifier redundant. It does so if:
+  **
+  **   1. The index is itself UNIQUE, and
+  **
+  **   2. All of the columns in the index are either part of the pDistinct
+  **      list, or else the WHERE clause contains a term of the form "col=X",
+  **      where X is a constant value. The collation sequences of the
+  **      comparison and select-list expressions must match those of the index.
+  **
+  **   3. All of those index columns for which the WHERE clause does not
+  **      contain a "col=X" term are subject to a NOT NULL constraint.
+  */
+  for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
+    if( !IsUniqueIndex(pIdx) ) continue;
+    for(i=0; i<pIdx->nKeyCol; i++){
+      i16 iCol = pIdx->aiColumn[i];
+      if( 0==findTerm(pWC, iBase, iCol, ~(Bitmask)0, WO_EQ, pIdx) ){
+        int iIdxCol = findIndexCol(pParse, pDistinct, iBase, pIdx, i);
+        if( iIdxCol<0 || pTab->aCol[iCol].notNull==0 ){
+          break;
+        }
+      }
+    }
+    if( i==pIdx->nKeyCol ){
+      /* This index implies that the DISTINCT qualifier is redundant. */
+      return 1;
+    }
+  }
+
+  return 0;
+}
+
+
+/*
+** Estimate the logarithm of the input value to base 2.
+*/
+static LogEst estLog(LogEst N){
+  return N<=10 ? 0 : sqlite3LogEst(N) - 33;
+}
+
+/*
+** 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(WHERETRACE_ENABLED)
+static void TRACE_IDX_INPUTS(sqlite3_index_info *p){
+  int i;
+  if( !sqlite3WhereTrace ) return;
+  for(i=0; i<p->nConstraint; i++){
+    sqlite3DebugPrintf("  constraint[%d]: col=%d termid=%d op=%d usabled=%d\n",
+       i,
+       p->aConstraint[i].iColumn,
+       p->aConstraint[i].iTermOffset,
+       p->aConstraint[i].op,
+       p->aConstraint[i].usable);
+  }
+  for(i=0; i<p->nOrderBy; i++){
+    sqlite3DebugPrintf("  orderby[%d]: col=%d desc=%d\n",
+       i,
+       p->aOrderBy[i].iColumn,
+       p->aOrderBy[i].desc);
+  }
+}
+static void TRACE_IDX_OUTPUTS(sqlite3_index_info *p){
+  int i;
+  if( !sqlite3WhereTrace ) return;
+  for(i=0; i<p->nConstraint; i++){
+    sqlite3DebugPrintf("  usage[%d]: argvIdx=%d omit=%d\n",
+       i,
+       p->aConstraintUsage[i].argvIndex,
+       p->aConstraintUsage[i].omit);
+  }
+  sqlite3DebugPrintf("  idxNum=%d\n", p->idxNum);
+  sqlite3DebugPrintf("  idxStr=%s\n", p->idxStr);
+  sqlite3DebugPrintf("  orderByConsumed=%d\n", p->orderByConsumed);
+  sqlite3DebugPrintf("  estimatedCost=%g\n", p->estimatedCost);
+  sqlite3DebugPrintf("  estimatedRows=%lld\n", p->estimatedRows);
+}
+#else
+#define TRACE_IDX_INPUTS(A)
+#define TRACE_IDX_OUTPUTS(A)
+#endif
+
+#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
+/*
+** Return TRUE if the WHERE clause term pTerm is of a form where it
+** could be used with an index to access pSrc, assuming an appropriate
+** index existed.
+*/
+static int termCanDriveIndex(
+  WhereTerm *pTerm,              /* WHERE clause term to check */
+  struct SrcList_item *pSrc,     /* Table we are trying to access */
+  Bitmask notReady               /* Tables in outer loops of the join */
+){
+  char aff;
+  if( pTerm->leftCursor!=pSrc->iCursor ) return 0;
+  if( (pTerm->eOperator & WO_EQ)==0 ) return 0;
+  if( (pTerm->prereqRight & notReady)!=0 ) return 0;
+  if( pTerm->u.leftColumn<0 ) return 0;
+  aff = pSrc->pTab->aCol[pTerm->u.leftColumn].affinity;
+  if( !sqlite3IndexAffinityOk(pTerm->pExpr, aff) ) return 0;
+  return 1;
+}
+#endif
+
+
+#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
+/*
+** Generate code to construct the Index object for an automatic index
+** and to set up the WhereLevel object pLevel so that the code generator
+** makes use of the automatic index.
+*/
+static void constructAutomaticIndex(
+  Parse *pParse,              /* The parsing context */
+  WhereClause *pWC,           /* The WHERE clause */
+  struct SrcList_item *pSrc,  /* The FROM clause term to get the next index */
+  Bitmask notReady,           /* Mask of cursors that are not available */
+  WhereLevel *pLevel          /* Write new index here */
+){
+  int nKeyCol;                /* Number of columns in the constructed index */
+  WhereTerm *pTerm;           /* A single term of the WHERE clause */
+  WhereTerm *pWCEnd;          /* End of pWC->a[] */
+  Index *pIdx;                /* Object describing the transient index */
+  Vdbe *v;                    /* Prepared statement under construction */
+  int addrInit;               /* Address of the initialization bypass jump */
+  Table *pTable;              /* The table being indexed */
+  int addrTop;                /* Top of the index fill loop */
+  int regRecord;              /* Register holding an index record */
+  int n;                      /* Column counter */
+  int i;                      /* Loop counter */
+  int mxBitCol;               /* Maximum column in pSrc->colUsed */
+  CollSeq *pColl;             /* Collating sequence to on a column */
+  WhereLoop *pLoop;           /* The Loop object */
+  char *zNotUsed;             /* Extra space on the end of pIdx */
+  Bitmask idxCols;            /* Bitmap of columns used for indexing */
+  Bitmask extraCols;          /* Bitmap of additional columns */
+  u8 sentWarning = 0;         /* True if a warnning has been issued */
+
+  /* Generate code to skip over the creation and initialization of the
+  ** transient index on 2nd and subsequent iterations of the loop. */
+  v = pParse->pVdbe;
+  assert( v!=0 );
+  addrInit = sqlite3CodeOnce(pParse); VdbeCoverage(v);
+
+  /* Count the number of columns that will be added to the index
+  ** and used to match WHERE clause constraints */
+  nKeyCol = 0;
+  pTable = pSrc->pTab;
+  pWCEnd = &pWC->a[pWC->nTerm];
+  pLoop = pLevel->pWLoop;
+  idxCols = 0;
+  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
+    if( termCanDriveIndex(pTerm, pSrc, notReady) ){
+      int iCol = pTerm->u.leftColumn;
+      Bitmask cMask = iCol>=BMS ? MASKBIT(BMS-1) : MASKBIT(iCol);
+      testcase( iCol==BMS );
+      testcase( iCol==BMS-1 );
+      if( !sentWarning ){
+        sqlite3_log(SQLITE_WARNING_AUTOINDEX,
+            "automatic index on %s(%s)", pTable->zName,
+            pTable->aCol[iCol].zName);
+        sentWarning = 1;
+      }
+      if( (idxCols & cMask)==0 ){
+        if( whereLoopResize(pParse->db, pLoop, nKeyCol+1) ) return;
+        pLoop->aLTerm[nKeyCol++] = pTerm;
+        idxCols |= cMask;
+      }
+    }
+  }
+  assert( nKeyCol>0 );
+  pLoop->u.btree.nEq = pLoop->nLTerm = nKeyCol;
+  pLoop->wsFlags = WHERE_COLUMN_EQ | WHERE_IDX_ONLY | WHERE_INDEXED
+                     | WHERE_AUTO_INDEX;
+
+  /* Count the number of additional columns needed to create a
+  ** covering index.  A "covering index" is an index that contains all
+  ** columns that are needed by the query.  With a covering index, the
+  ** original table never needs to be accessed.  Automatic indices must
+  ** be a covering index because the index will not be updated if the
+  ** original table changes and the index and table cannot both be used
+  ** if they go out of sync.
+  */
+  extraCols = pSrc->colUsed & (~idxCols | MASKBIT(BMS-1));
+  mxBitCol = (pTable->nCol >= BMS-1) ? BMS-1 : pTable->nCol;
+  testcase( pTable->nCol==BMS-1 );
+  testcase( pTable->nCol==BMS-2 );
+  for(i=0; i<mxBitCol; i++){
+    if( extraCols & MASKBIT(i) ) nKeyCol++;
+  }
+  if( pSrc->colUsed & MASKBIT(BMS-1) ){
+    nKeyCol += pTable->nCol - BMS + 1;
+  }
+  pLoop->wsFlags |= WHERE_COLUMN_EQ | WHERE_IDX_ONLY;
+
+  /* Construct the Index object to describe this index */
+  pIdx = sqlite3AllocateIndexObject(pParse->db, nKeyCol+1, 0, &zNotUsed);
+  if( pIdx==0 ) return;
+  pLoop->u.btree.pIndex = pIdx;
+  pIdx->zName = "auto-index";
+  pIdx->pTable = pTable;
+  n = 0;
+  idxCols = 0;
+  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
+    if( termCanDriveIndex(pTerm, pSrc, notReady) ){
+      int iCol = pTerm->u.leftColumn;
+      Bitmask cMask = iCol>=BMS ? MASKBIT(BMS-1) : MASKBIT(iCol);
+      testcase( iCol==BMS-1 );
+      testcase( iCol==BMS );
+      if( (idxCols & cMask)==0 ){
+        Expr *pX = pTerm->pExpr;
+        idxCols |= cMask;
+        pIdx->aiColumn[n] = pTerm->u.leftColumn;
+        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
+        pIdx->azColl[n] = ALWAYS(pColl) ? pColl->zName : "BINARY";
+        n++;
+      }
+    }
+  }
+  assert( (u32)n==pLoop->u.btree.nEq );
+
+  /* Add additional columns needed to make the automatic index into
+  ** a covering index */
+  for(i=0; i<mxBitCol; i++){
+    if( extraCols & MASKBIT(i) ){
+      pIdx->aiColumn[n] = i;
+      pIdx->azColl[n] = "BINARY";
+      n++;
+    }
+  }
+  if( pSrc->colUsed & MASKBIT(BMS-1) ){
+    for(i=BMS-1; i<pTable->nCol; i++){
+      pIdx->aiColumn[n] = i;
+      pIdx->azColl[n] = "BINARY";
+      n++;
+    }
+  }
+  assert( n==nKeyCol );
+  pIdx->aiColumn[n] = -1;
+  pIdx->azColl[n] = "BINARY";
+
+  /* Create the automatic index */
+  assert( pLevel->iIdxCur>=0 );
+  pLevel->iIdxCur = pParse->nTab++;
+  sqlite3VdbeAddOp2(v, OP_OpenAutoindex, pLevel->iIdxCur, nKeyCol+1);
+  sqlite3VdbeSetP4KeyInfo(pParse, pIdx);
+  VdbeComment((v, "for %s", pTable->zName));
+
+  /* Fill the automatic index with content */
+  addrTop = sqlite3VdbeAddOp1(v, OP_Rewind, pLevel->iTabCur); VdbeCoverage(v);
+  regRecord = sqlite3GetTempReg(pParse);
+  sqlite3GenerateIndexKey(pParse, pIdx, pLevel->iTabCur, regRecord, 0, 0, 0, 0);
+  sqlite3VdbeAddOp2(v, OP_IdxInsert, pLevel->iIdxCur, regRecord);
+  sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);
+  sqlite3VdbeAddOp2(v, OP_Next, pLevel->iTabCur, addrTop+1); VdbeCoverage(v);
+  sqlite3VdbeChangeP5(v, SQLITE_STMTSTATUS_AUTOINDEX);
+  sqlite3VdbeJumpHere(v, addrTop);
+  sqlite3ReleaseTempReg(pParse, regRecord);
+  
+  /* Jump here when skipping the initialization */
+  sqlite3VdbeJumpHere(v, addrInit);
+}
+#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */
+
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+/*
+** Allocate and populate an sqlite3_index_info structure. It is the 
+** responsibility of the caller to eventually release the structure
+** by passing the pointer returned by this function to sqlite3_free().
+*/
+static sqlite3_index_info *allocateIndexInfo(
+  Parse *pParse,
+  WhereClause *pWC,
+  struct SrcList_item *pSrc,
+  ExprList *pOrderBy
+){
+  int i, j;
+  int nTerm;
+  struct sqlite3_index_constraint *pIdxCons;
+  struct sqlite3_index_orderby *pIdxOrderBy;
+  struct sqlite3_index_constraint_usage *pUsage;
+  WhereTerm *pTerm;
+  int nOrderBy;
+  sqlite3_index_info *pIdxInfo;
+
+  /* Count the number of possible WHERE clause constraints referring
+  ** to this virtual table */
+  for(i=nTerm=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
+    if( pTerm->leftCursor != pSrc->iCursor ) continue;
+    assert( IsPowerOfTwo(pTerm->eOperator & ~WO_EQUIV) );
+    testcase( pTerm->eOperator & WO_IN );
+    testcase( pTerm->eOperator & WO_ISNULL );
+    testcase( pTerm->eOperator & WO_ALL );
+    if( (pTerm->eOperator & ~(WO_ISNULL|WO_EQUIV))==0 ) continue;
+    if( pTerm->wtFlags & TERM_VNULL ) 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 ){
+    int n = pOrderBy->nExpr;
+    for(i=0; i<n; i++){
+      Expr *pExpr = pOrderBy->a[i].pExpr;
+      if( pExpr->op!=TK_COLUMN || pExpr->iTable!=pSrc->iCursor ) break;
+    }
+    if( i==n){
+      nOrderBy = n;
+    }
+  }
+
+  /* Allocate the sqlite3_index_info structure
+  */
+  pIdxInfo = sqlite3DbMallocZero(pParse->db, sizeof(*pIdxInfo)
+                           + (sizeof(*pIdxCons) + sizeof(*pUsage))*nTerm
+                           + sizeof(*pIdxOrderBy)*nOrderBy );
+  if( pIdxInfo==0 ){
+    sqlite3ErrorMsg(pParse, "out of memory");
+    return 0;
+  }
+
+  /* Initialize the structure.  The sqlite3_index_info structure contains
+  ** many fields that are declared "const" to prevent xBestIndex from
+  ** changing them.  We have to do some funky casting in order to
+  ** initialize those fields.
+  */
+  pIdxCons = (struct sqlite3_index_constraint*)&pIdxInfo[1];
+  pIdxOrderBy = (struct sqlite3_index_orderby*)&pIdxCons[nTerm];
+  pUsage = (struct sqlite3_index_constraint_usage*)&pIdxOrderBy[nOrderBy];
+  *(int*)&pIdxInfo->nConstraint = nTerm;
+  *(int*)&pIdxInfo->nOrderBy = nOrderBy;
+  *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint = pIdxCons;
+  *(struct sqlite3_index_orderby**)&pIdxInfo->aOrderBy = pIdxOrderBy;
+  *(struct sqlite3_index_constraint_usage**)&pIdxInfo->aConstraintUsage =
+                                                                   pUsage;
+
+  for(i=j=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
+    u8 op;
+    if( pTerm->leftCursor != pSrc->iCursor ) continue;
+    assert( IsPowerOfTwo(pTerm->eOperator & ~WO_EQUIV) );
+    testcase( pTerm->eOperator & WO_IN );
+    testcase( pTerm->eOperator & WO_ISNULL );
+    testcase( pTerm->eOperator & WO_ALL );
+    if( (pTerm->eOperator & ~(WO_ISNULL|WO_EQUIV))==0 ) continue;
+    if( pTerm->wtFlags & TERM_VNULL ) continue;
+    pIdxCons[j].iColumn = pTerm->u.leftColumn;
+    pIdxCons[j].iTermOffset = i;
+    op = (u8)pTerm->eOperator & WO_ALL;
+    if( op==WO_IN ) op = WO_EQ;
+    pIdxCons[j].op = op;
+    /* 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_IN|WO_EQ|WO_LT|WO_LE|WO_GT|WO_GE|WO_MATCH) );
+    j++;
+  }
+  for(i=0; i<nOrderBy; i++){
+    Expr *pExpr = pOrderBy->a[i].pExpr;
+    pIdxOrderBy[i].iColumn = pExpr->iColumn;
+    pIdxOrderBy[i].desc = pOrderBy->a[i].sortOrder;
+  }
+
+  return pIdxInfo;
+}
+
+/*
+** The table object reference passed as the second argument to this function
+** must represent a virtual table. This function invokes the xBestIndex()
+** method of the virtual table with the sqlite3_index_info object that
+** comes in as the 3rd argument to this function.
+**
+** If an error occurs, pParse is populated with an error message and a
+** non-zero value is returned. Otherwise, 0 is returned and the output
+** part of the sqlite3_index_info structure is left populated.
+**
+** Whether or not an error is returned, it is the responsibility of the
+** caller to eventually free p->idxStr if p->needToFreeIdxStr indicates
+** that this is required.
+*/
+static int vtabBestIndex(Parse *pParse, Table *pTab, sqlite3_index_info *p){
+  sqlite3_vtab *pVtab = sqlite3GetVTable(pParse->db, pTab)->pVtab;
+  int i;
+  int rc;
+
+  TRACE_IDX_INPUTS(p);
+  rc = pVtab->pModule->xBestIndex(pVtab, p);
+  TRACE_IDX_OUTPUTS(p);
+
+  if( rc!=SQLITE_OK ){
+    if( rc==SQLITE_NOMEM ){
+      pParse->db->mallocFailed = 1;
+    }else if( !pVtab->zErrMsg ){
+      sqlite3ErrorMsg(pParse, "%s", sqlite3ErrStr(rc));
+    }else{
+      sqlite3ErrorMsg(pParse, "%s", pVtab->zErrMsg);
+    }
+  }
+  sqlite3_free(pVtab->zErrMsg);
+  pVtab->zErrMsg = 0;
+
+  for(i=0; i<p->nConstraint; i++){
+    if( !p->aConstraint[i].usable && p->aConstraintUsage[i].argvIndex>0 ){
+      sqlite3ErrorMsg(pParse, 
+          "table %s: xBestIndex returned an invalid plan", pTab->zName);
+    }
+  }
+
+  return pParse->nErr;
+}
+#endif /* !defined(SQLITE_OMIT_VIRTUALTABLE) */
+
+
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+/*
+** Estimate the location of a particular key among all keys in an
+** index.  Store the results in aStat as follows:
+**
+**    aStat[0]      Est. number of rows less than pVal
+**    aStat[1]      Est. number of rows equal to pVal
+**
+** Return SQLITE_OK on success.
+*/
+static void whereKeyStats(
+  Parse *pParse,              /* Database connection */
+  Index *pIdx,                /* Index to consider domain of */
+  UnpackedRecord *pRec,       /* Vector of values to consider */
+  int roundUp,                /* Round up if true.  Round down if false */
+  tRowcnt *aStat              /* OUT: stats written here */
+){
+  IndexSample *aSample = pIdx->aSample;
+  int iCol;                   /* Index of required stats in anEq[] etc. */
+  int iMin = 0;               /* Smallest sample not yet tested */
+  int i = pIdx->nSample;      /* Smallest sample larger than or equal to pRec */
+  int iTest;                  /* Next sample to test */
+  int res;                    /* Result of comparison operation */
+
+#ifndef SQLITE_DEBUG
+  UNUSED_PARAMETER( pParse );
+#endif
+  assert( pRec!=0 );
+  iCol = pRec->nField - 1;
+  assert( pIdx->nSample>0 );
+  assert( pRec->nField>0 && iCol<pIdx->nSampleCol );
+  do{
+    iTest = (iMin+i)/2;
+    res = sqlite3VdbeRecordCompare(aSample[iTest].n, aSample[iTest].p, pRec);
+    if( res<0 ){
+      iMin = iTest+1;
+    }else{
+      i = iTest;
+    }
+  }while( res && iMin<i );
+
+#ifdef SQLITE_DEBUG
+  /* The following assert statements check that the binary search code
+  ** above found the right answer. This block serves no purpose other
+  ** than to invoke the asserts.  */
+  if( res==0 ){
+    /* If (res==0) is true, then sample $i must be equal to pRec */
+    assert( i<pIdx->nSample );
+    assert( 0==sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec)
+         || pParse->db->mallocFailed );
+  }else{
+    /* Otherwise, pRec must be smaller than sample $i and larger than
+    ** sample ($i-1).  */
+    assert( i==pIdx->nSample 
+         || sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec)>0
+         || pParse->db->mallocFailed );
+    assert( i==0
+         || sqlite3VdbeRecordCompare(aSample[i-1].n, aSample[i-1].p, pRec)<0
+         || pParse->db->mallocFailed );
+  }
+#endif /* ifdef SQLITE_DEBUG */
+
+  /* At this point, aSample[i] is the first sample that is greater than
+  ** or equal to pVal.  Or if i==pIdx->nSample, then all samples are less
+  ** than pVal.  If aSample[i]==pVal, then res==0.
+  */
+  if( res==0 ){
+    aStat[0] = aSample[i].anLt[iCol];
+    aStat[1] = aSample[i].anEq[iCol];
+  }else{
+    tRowcnt iLower, iUpper, iGap;
+    if( i==0 ){
+      iLower = 0;
+      iUpper = aSample[0].anLt[iCol];
+    }else{
+      i64 nRow0 = sqlite3LogEstToInt(pIdx->aiRowLogEst[0]);
+      iUpper = i>=pIdx->nSample ? nRow0 : aSample[i].anLt[iCol];
+      iLower = aSample[i-1].anEq[iCol] + aSample[i-1].anLt[iCol];
+    }
+    aStat[1] = pIdx->aAvgEq[iCol];
+    if( iLower>=iUpper ){
+      iGap = 0;
+    }else{
+      iGap = iUpper - iLower;
+    }
+    if( roundUp ){
+      iGap = (iGap*2)/3;
+    }else{
+      iGap = iGap/3;
+    }
+    aStat[0] = iLower + iGap;
+  }
+}
+#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
+
+/*
+** If it is not NULL, pTerm is a term that provides an upper or lower
+** bound on a range scan. Without considering pTerm, it is estimated 
+** that the scan will visit nNew rows. This function returns the number
+** estimated to be visited after taking pTerm into account.
+**
+** If the user explicitly specified a likelihood() value for this term,
+** then the return value is the likelihood multiplied by the number of
+** input rows. Otherwise, this function assumes that an "IS NOT NULL" term
+** has a likelihood of 0.50, and any other term a likelihood of 0.25.
+*/
+static LogEst whereRangeAdjust(WhereTerm *pTerm, LogEst nNew){
+  LogEst nRet = nNew;
+  if( pTerm ){
+    if( pTerm->truthProb<=0 ){
+      nRet += pTerm->truthProb;
+    }else if( (pTerm->wtFlags & TERM_VNULL)==0 ){
+      nRet -= 20;        assert( 20==sqlite3LogEst(4) );
+    }
+  }
+  return nRet;
+}
+
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+/* 
+** This function is called to estimate the number of rows visited by a
+** range-scan on a skip-scan index. For example:
+**
+**   CREATE INDEX i1 ON t1(a, b, c);
+**   SELECT * FROM t1 WHERE a=? AND c BETWEEN ? AND ?;
+**
+** Value pLoop->nOut is currently set to the estimated number of rows 
+** visited for scanning (a=? AND b=?). This function reduces that estimate 
+** by some factor to account for the (c BETWEEN ? AND ?) expression based
+** on the stat4 data for the index. this scan will be peformed multiple 
+** times (once for each (a,b) combination that matches a=?) is dealt with 
+** by the caller.
+**
+** It does this by scanning through all stat4 samples, comparing values
+** extracted from pLower and pUpper with the corresponding column in each
+** sample. If L and U are the number of samples found to be less than or
+** equal to the values extracted from pLower and pUpper respectively, and
+** N is the total number of samples, the pLoop->nOut value is adjusted
+** as follows:
+**
+**   nOut = nOut * ( min(U - L, 1) / N )
+**
+** If pLower is NULL, or a value cannot be extracted from the term, L is
+** set to zero. If pUpper is NULL, or a value cannot be extracted from it,
+** U is set to N.
+**
+** Normally, this function sets *pbDone to 1 before returning. However,
+** if no value can be extracted from either pLower or pUpper (and so the
+** estimate of the number of rows delivered remains unchanged), *pbDone
+** is left as is.
+**
+** If an error occurs, an SQLite error code is returned. Otherwise, 
+** SQLITE_OK.
+*/
+static int whereRangeSkipScanEst(
+  Parse *pParse,       /* Parsing & code generating context */
+  WhereTerm *pLower,   /* Lower bound on the range. ex: "x>123" Might be NULL */
+  WhereTerm *pUpper,   /* Upper bound on the range. ex: "x<455" Might be NULL */
+  WhereLoop *pLoop,    /* Update the .nOut value of this loop */
+  int *pbDone          /* Set to true if at least one expr. value extracted */
+){
+  Index *p = pLoop->u.btree.pIndex;
+  int nEq = pLoop->u.btree.nEq;
+  sqlite3 *db = pParse->db;
+  int nLower = -1;
+  int nUpper = p->nSample+1;
+  int rc = SQLITE_OK;
+  int iCol = p->aiColumn[nEq];
+  u8 aff = iCol>=0 ? p->pTable->aCol[iCol].affinity : SQLITE_AFF_INTEGER;
+  CollSeq *pColl;
+  
+  sqlite3_value *p1 = 0;          /* Value extracted from pLower */
+  sqlite3_value *p2 = 0;          /* Value extracted from pUpper */
+  sqlite3_value *pVal = 0;        /* Value extracted from record */
+
+  pColl = sqlite3LocateCollSeq(pParse, p->azColl[nEq]);
+  if( pLower ){
+    rc = sqlite3Stat4ValueFromExpr(pParse, pLower->pExpr->pRight, aff, &p1);
+    nLower = 0;
+  }
+  if( pUpper && rc==SQLITE_OK ){
+    rc = sqlite3Stat4ValueFromExpr(pParse, pUpper->pExpr->pRight, aff, &p2);
+    nUpper = p2 ? 0 : p->nSample;
+  }
+
+  if( p1 || p2 ){
+    int i;
+    int nDiff;
+    for(i=0; rc==SQLITE_OK && i<p->nSample; i++){
+      rc = sqlite3Stat4Column(db, p->aSample[i].p, p->aSample[i].n, nEq, &pVal);
+      if( rc==SQLITE_OK && p1 ){
+        int res = sqlite3MemCompare(p1, pVal, pColl);
+        if( res>=0 ) nLower++;
+      }
+      if( rc==SQLITE_OK && p2 ){
+        int res = sqlite3MemCompare(p2, pVal, pColl);
+        if( res>=0 ) nUpper++;
+      }
+    }
+    nDiff = (nUpper - nLower);
+    if( nDiff<=0 ) nDiff = 1;
+
+    /* If there is both an upper and lower bound specified, and the 
+    ** comparisons indicate that they are close together, use the fallback
+    ** method (assume that the scan visits 1/64 of the rows) for estimating
+    ** the number of rows visited. Otherwise, estimate the number of rows
+    ** using the method described in the header comment for this function. */
+    if( nDiff!=1 || pUpper==0 || pLower==0 ){
+      int nAdjust = (sqlite3LogEst(p->nSample) - sqlite3LogEst(nDiff));
+      pLoop->nOut -= nAdjust;
+      *pbDone = 1;
+      WHERETRACE(0x10, ("range skip-scan regions: %u..%u  adjust=%d est=%d\n",
+                           nLower, nUpper, nAdjust*-1, pLoop->nOut));
+    }
+
+  }else{
+    assert( *pbDone==0 );
+  }
+
+  sqlite3ValueFree(p1);
+  sqlite3ValueFree(p2);
+  sqlite3ValueFree(pVal);
+
+  return rc;
+}
+#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
+
+/*
+** This function is used to estimate the number of rows that will be visited
+** by scanning an index for a range of values. The range may have an upper
+** bound, a lower bound, or both. The WHERE clause terms that set the upper
+** and lower bounds are represented by pLower and pUpper respectively. For
+** example, assuming that index p is on t1(a):
+**
+**   ... FROM t1 WHERE a > ? AND a < ? ...
+**                    |_____|   |_____|
+**                       |         |
+**                     pLower    pUpper
+**
+** If either of the upper or lower bound is not present, then NULL is passed in
+** place of the corresponding WhereTerm.
+**
+** The value in (pBuilder->pNew->u.btree.nEq) is the index of the index
+** column subject to the range constraint. Or, equivalently, the number of
+** equality constraints optimized by the proposed index scan. For example,
+** assuming index p is on t1(a, b), and the SQL query is:
+**
+**   ... FROM t1 WHERE a = ? AND b > ? AND b < ? ...
+**
+** then nEq is set to 1 (as the range restricted column, b, is the second 
+** left-most column of the index). Or, if the query is:
+**
+**   ... FROM t1 WHERE a > ? AND a < ? ...
+**
+** then nEq is set to 0.
+**
+** When this function is called, *pnOut is set to the sqlite3LogEst() of the
+** number of rows that the index scan is expected to visit without 
+** considering the range constraints. If nEq is 0, this is the number of 
+** rows in the index. Assuming no error occurs, *pnOut is adjusted (reduced)
+** to account for the range constraints pLower and pUpper.
+** 
+** In the absence of sqlite_stat4 ANALYZE data, or if such data cannot be
+** used, a single range inequality reduces the search space by a factor of 4. 
+** and a pair of constraints (x>? AND x<?) reduces the expected number of
+** rows visited by a factor of 64.
+*/
+static int whereRangeScanEst(
+  Parse *pParse,       /* Parsing & code generating context */
+  WhereLoopBuilder *pBuilder,
+  WhereTerm *pLower,   /* Lower bound on the range. ex: "x>123" Might be NULL */
+  WhereTerm *pUpper,   /* Upper bound on the range. ex: "x<455" Might be NULL */
+  WhereLoop *pLoop     /* Modify the .nOut and maybe .rRun fields */
+){
+  int rc = SQLITE_OK;
+  int nOut = pLoop->nOut;
+  LogEst nNew;
+
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+  Index *p = pLoop->u.btree.pIndex;
+  int nEq = pLoop->u.btree.nEq;
+
+  if( p->nSample>0
+   && nEq<p->nSampleCol
+   && OptimizationEnabled(pParse->db, SQLITE_Stat3) 
+  ){
+    if( nEq==pBuilder->nRecValid ){
+      UnpackedRecord *pRec = pBuilder->pRec;
+      tRowcnt a[2];
+      u8 aff;
+
+      /* Variable iLower will be set to the estimate of the number of rows in 
+      ** the index that are less than the lower bound of the range query. The
+      ** lower bound being the concatenation of $P and $L, where $P is the
+      ** key-prefix formed by the nEq values matched against the nEq left-most
+      ** columns of the index, and $L is the value in pLower.
+      **
+      ** Or, if pLower is NULL or $L cannot be extracted from it (because it
+      ** is not a simple variable or literal value), the lower bound of the
+      ** range is $P. Due to a quirk in the way whereKeyStats() works, even
+      ** if $L is available, whereKeyStats() is called for both ($P) and 
+      ** ($P:$L) and the larger of the two returned values used.
+      **
+      ** Similarly, iUpper is to be set to the estimate of the number of rows
+      ** less than the upper bound of the range query. Where the upper bound
+      ** is either ($P) or ($P:$U). Again, even if $U is available, both values
+      ** of iUpper are requested of whereKeyStats() and the smaller used.
+      */
+      tRowcnt iLower;
+      tRowcnt iUpper;
+
+      if( pRec ){
+        testcase( pRec->nField!=pBuilder->nRecValid );
+        pRec->nField = pBuilder->nRecValid;
+      }
+      if( nEq==p->nKeyCol ){
+        aff = SQLITE_AFF_INTEGER;
+      }else{
+        aff = p->pTable->aCol[p->aiColumn[nEq]].affinity;
+      }
+      /* Determine iLower and iUpper using ($P) only. */
+      if( nEq==0 ){
+        iLower = 0;
+        iUpper = sqlite3LogEstToInt(p->aiRowLogEst[0]);
+      }else{
+        /* Note: this call could be optimized away - since the same values must 
+        ** have been requested when testing key $P in whereEqualScanEst().  */
+        whereKeyStats(pParse, p, pRec, 0, a);
+        iLower = a[0];
+        iUpper = a[0] + a[1];
+      }
+
+      assert( pLower==0 || (pLower->eOperator & (WO_GT|WO_GE))!=0 );
+      assert( pUpper==0 || (pUpper->eOperator & (WO_LT|WO_LE))!=0 );
+      assert( p->aSortOrder!=0 );
+      if( p->aSortOrder[nEq] ){
+        /* The roles of pLower and pUpper are swapped for a DESC index */
+        SWAP(WhereTerm*, pLower, pUpper);
+      }
+
+      /* If possible, improve on the iLower estimate using ($P:$L). */
+      if( pLower ){
+        int bOk;                    /* True if value is extracted from pExpr */
+        Expr *pExpr = pLower->pExpr->pRight;
+        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
+        if( rc==SQLITE_OK && bOk ){
+          tRowcnt iNew;
+          whereKeyStats(pParse, p, pRec, 0, a);
+          iNew = a[0] + ((pLower->eOperator & (WO_GT|WO_LE)) ? a[1] : 0);
+          if( iNew>iLower ) iLower = iNew;
+          nOut--;
+          pLower = 0;
+        }
+      }
+
+      /* If possible, improve on the iUpper estimate using ($P:$U). */
+      if( pUpper ){
+        int bOk;                    /* True if value is extracted from pExpr */
+        Expr *pExpr = pUpper->pExpr->pRight;
+        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
+        if( rc==SQLITE_OK && bOk ){
+          tRowcnt iNew;
+          whereKeyStats(pParse, p, pRec, 1, a);
+          iNew = a[0] + ((pUpper->eOperator & (WO_GT|WO_LE)) ? a[1] : 0);
+          if( iNew<iUpper ) iUpper = iNew;
+          nOut--;
+          pUpper = 0;
+        }
+      }
+
+      pBuilder->pRec = pRec;
+      if( rc==SQLITE_OK ){
+        if( iUpper>iLower ){
+          nNew = sqlite3LogEst(iUpper - iLower);
+        }else{
+          nNew = 10;        assert( 10==sqlite3LogEst(2) );
+        }
+        if( nNew<nOut ){
+          nOut = nNew;
+        }
+        WHERETRACE(0x10, ("STAT4 range scan: %u..%u  est=%d\n",
+                           (u32)iLower, (u32)iUpper, nOut));
+      }
+    }else{
+      int bDone = 0;
+      rc = whereRangeSkipScanEst(pParse, pLower, pUpper, pLoop, &bDone);
+      if( bDone ) return rc;
+    }
+  }
+#else
+  UNUSED_PARAMETER(pParse);
+  UNUSED_PARAMETER(pBuilder);
+  assert( pLower || pUpper );
+#endif
+  assert( pUpper==0 || (pUpper->wtFlags & TERM_VNULL)==0 );
+  nNew = whereRangeAdjust(pLower, nOut);
+  nNew = whereRangeAdjust(pUpper, nNew);
+
+  /* TUNING: If there is both an upper and lower limit, assume the range is
+  ** reduced by an additional 75%. This means that, by default, an open-ended
+  ** range query (e.g. col > ?) is assumed to match 1/4 of the rows in the
+  ** index. While a closed range (e.g. col BETWEEN ? AND ?) is estimated to
+  ** match 1/64 of the index. */ 
+  if( pLower && pUpper ) nNew -= 20;
+
+  nOut -= (pLower!=0) + (pUpper!=0);
+  if( nNew<10 ) nNew = 10;
+  if( nNew<nOut ) nOut = nNew;
+#if defined(WHERETRACE_ENABLED)
+  if( pLoop->nOut>nOut ){
+    WHERETRACE(0x10,("Range scan lowers nOut from %d to %d\n",
+                    pLoop->nOut, nOut));
+  }
+#endif
+  pLoop->nOut = (LogEst)nOut;
+  return rc;
+}
+
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+/*
+** Estimate the number of rows that will be returned based on
+** an equality constraint x=VALUE and where that VALUE occurs in
+** the histogram data.  This only works when x is the left-most
+** column of an index and sqlite_stat3 histogram data is available
+** for that index.  When pExpr==NULL that means the constraint is
+** "x IS NULL" instead of "x=VALUE".
+**
+** Write the estimated row count into *pnRow and return SQLITE_OK. 
+** If unable to make an estimate, leave *pnRow unchanged and return
+** non-zero.
+**
+** This routine can fail if it is unable to load a collating sequence
+** required for string comparison, or if unable to allocate memory
+** for a UTF conversion required for comparison.  The error is stored
+** in the pParse structure.
+*/
+static int whereEqualScanEst(
+  Parse *pParse,       /* Parsing & code generating context */
+  WhereLoopBuilder *pBuilder,
+  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
+  tRowcnt *pnRow       /* Write the revised row estimate here */
+){
+  Index *p = pBuilder->pNew->u.btree.pIndex;
+  int nEq = pBuilder->pNew->u.btree.nEq;
+  UnpackedRecord *pRec = pBuilder->pRec;
+  u8 aff;                   /* Column affinity */
+  int rc;                   /* Subfunction return code */
+  tRowcnt a[2];             /* Statistics */
+  int bOk;
+
+  assert( nEq>=1 );
+  assert( nEq<=p->nColumn );
+  assert( p->aSample!=0 );
+  assert( p->nSample>0 );
+  assert( pBuilder->nRecValid<nEq );
+
+  /* If values are not available for all fields of the index to the left
+  ** of this one, no estimate can be made. Return SQLITE_NOTFOUND. */
+  if( pBuilder->nRecValid<(nEq-1) ){
+    return SQLITE_NOTFOUND;
+  }
+
+  /* This is an optimization only. The call to sqlite3Stat4ProbeSetValue()
+  ** below would return the same value.  */
+  if( nEq>=p->nColumn ){
+    *pnRow = 1;
+    return SQLITE_OK;
+  }
+
+  aff = p->pTable->aCol[p->aiColumn[nEq-1]].affinity;
+  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq-1, &bOk);
+  pBuilder->pRec = pRec;
+  if( rc!=SQLITE_OK ) return rc;
+  if( bOk==0 ) return SQLITE_NOTFOUND;
+  pBuilder->nRecValid = nEq;
+
+  whereKeyStats(pParse, p, pRec, 0, a);
+  WHERETRACE(0x10,("equality scan regions: %d\n", (int)a[1]));
+  *pnRow = a[1];
+  
+  return rc;
+}
+#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
+
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+/*
+** Estimate the number of rows that will be returned based on
+** an IN constraint where the right-hand side of the IN operator
+** is a list of values.  Example:
+**
+**        WHERE x IN (1,2,3,4)
+**
+** Write the estimated row count into *pnRow and return SQLITE_OK. 
+** If unable to make an estimate, leave *pnRow unchanged and return
+** non-zero.
+**
+** This routine can fail if it is unable to load a collating sequence
+** required for string comparison, or if unable to allocate memory
+** for a UTF conversion required for comparison.  The error is stored
+** in the pParse structure.
+*/
+static int whereInScanEst(
+  Parse *pParse,       /* Parsing & code generating context */
+  WhereLoopBuilder *pBuilder,
+  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
+  tRowcnt *pnRow       /* Write the revised row estimate here */
+){
+  Index *p = pBuilder->pNew->u.btree.pIndex;
+  i64 nRow0 = sqlite3LogEstToInt(p->aiRowLogEst[0]);
+  int nRecValid = pBuilder->nRecValid;
+  int rc = SQLITE_OK;     /* Subfunction return code */
+  tRowcnt nEst;           /* Number of rows for a single term */
+  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */
+  int i;                  /* Loop counter */
+
+  assert( p->aSample!=0 );
+  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
+    nEst = nRow0;
+    rc = whereEqualScanEst(pParse, pBuilder, pList->a[i].pExpr, &nEst);
+    nRowEst += nEst;
+    pBuilder->nRecValid = nRecValid;
+  }
+
+  if( rc==SQLITE_OK ){
+    if( nRowEst > nRow0 ) nRowEst = nRow0;
+    *pnRow = nRowEst;
+    WHERETRACE(0x10,("IN row estimate: est=%d\n", nRowEst));
+  }
+  assert( pBuilder->nRecValid==nRecValid );
+  return rc;
+}
+#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */
+
+/*
+** 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->wtFlags & TERM_CODED)==0
+      && (pLevel->iLeftJoin==0 || ExprHasProperty(pTerm->pExpr, EP_FromJoin))
+      && (pLevel->notReady & pTerm->prereqAll)==0
+  ){
+    pTerm->wtFlags |= TERM_CODED;
+    if( pTerm->iParent>=0 ){
+      WhereTerm *pOther = &pTerm->pWC->a[pTerm->iParent];
+      if( (--pOther->nChild)==0 ){
+        disableTerm(pLevel, pOther);
+      }
+    }
+  }
+}
+
+/*
+** Code an OP_Affinity opcode to apply the column affinity string zAff
+** to the n registers starting at base. 
+**
+** As an optimization, SQLITE_AFF_NONE entries (which are no-ops) at the
+** beginning and end of zAff are ignored.  If all entries in zAff are
+** SQLITE_AFF_NONE, then no code gets generated.
+**
+** This routine makes its own copy of zAff so that the caller is free
+** to modify zAff after this routine returns.
+*/
+static void codeApplyAffinity(Parse *pParse, int base, int n, char *zAff){
+  Vdbe *v = pParse->pVdbe;
+  if( zAff==0 ){
+    assert( pParse->db->mallocFailed );
+    return;
+  }
+  assert( v!=0 );
+
+  /* Adjust base and n to skip over SQLITE_AFF_NONE entries at the beginning
+  ** and end of the affinity string.
+  */
+  while( n>0 && zAff[0]==SQLITE_AFF_NONE ){
+    n--;
+    base++;
+    zAff++;
+  }
+  while( n>1 && zAff[n-1]==SQLITE_AFF_NONE ){
+    n--;
+  }
+
+  /* Code the OP_Affinity opcode if there is anything left to do. */
+  if( n>0 ){
+    sqlite3VdbeAddOp2(v, OP_Affinity, base, n);
+    sqlite3VdbeChangeP4(v, -1, zAff, n);
+    sqlite3ExprCacheAffinityChange(pParse, base, n);
+  }
+}
+
+
+/*
+** Generate code for a single equality term of the WHERE clause.  An equality
+** term can be either X=expr or X IN (...).   pTerm is the term to be 
+** coded.
+**
+** The current value for the constraint is left in register iReg.
+**
+** For a constraint of the form X=expr, the expression is evaluated and its
+** result is left on the stack.  For constraints of the form X IN (...)
+** this routine sets up a loop that will iterate over all values of X.
+*/
+static int codeEqualityTerm(
+  Parse *pParse,      /* The parsing context */
+  WhereTerm *pTerm,   /* The term of the WHERE clause to be coded */
+  WhereLevel *pLevel, /* The level of the FROM clause we are working on */
+  int iEq,            /* Index of the equality term within this level */
+  int bRev,           /* True for reverse-order IN operations */
+  int iTarget         /* Attempt to leave results in this register */
+){
+  Expr *pX = pTerm->pExpr;
+  Vdbe *v = pParse->pVdbe;
+  int iReg;                  /* Register holding results */
+
+  assert( iTarget>0 );
+  if( pX->op==TK_EQ ){
+    iReg = sqlite3ExprCodeTarget(pParse, pX->pRight, iTarget);
+  }else if( pX->op==TK_ISNULL ){
+    iReg = iTarget;
+    sqlite3VdbeAddOp2(v, OP_Null, 0, iReg);
+#ifndef SQLITE_OMIT_SUBQUERY
+  }else{
+    int eType;
+    int iTab;
+    struct InLoop *pIn;
+    WhereLoop *pLoop = pLevel->pWLoop;
+
+    if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0
+      && pLoop->u.btree.pIndex!=0
+      && pLoop->u.btree.pIndex->aSortOrder[iEq]
+    ){
+      testcase( iEq==0 );
+      testcase( bRev );
+      bRev = !bRev;
+    }
+    assert( pX->op==TK_IN );
+    iReg = iTarget;
+    eType = sqlite3FindInIndex(pParse, pX, IN_INDEX_LOOP, 0);
+    if( eType==IN_INDEX_INDEX_DESC ){
+      testcase( bRev );
+      bRev = !bRev;
+    }
+    iTab = pX->iTable;
+    sqlite3VdbeAddOp2(v, bRev ? OP_Last : OP_Rewind, iTab, 0);
+    VdbeCoverageIf(v, bRev);
+    VdbeCoverageIf(v, !bRev);
+    assert( (pLoop->wsFlags & WHERE_MULTI_OR)==0 );
+    pLoop->wsFlags |= WHERE_IN_ABLE;
+    if( pLevel->u.in.nIn==0 ){
+      pLevel->addrNxt = sqlite3VdbeMakeLabel(v);
+    }
+    pLevel->u.in.nIn++;
+    pLevel->u.in.aInLoop =
+       sqlite3DbReallocOrFree(pParse->db, pLevel->u.in.aInLoop,
+                              sizeof(pLevel->u.in.aInLoop[0])*pLevel->u.in.nIn);
+    pIn = pLevel->u.in.aInLoop;
+    if( pIn ){
+      pIn += pLevel->u.in.nIn - 1;
+      pIn->iCur = iTab;
+      if( eType==IN_INDEX_ROWID ){
+        pIn->addrInTop = sqlite3VdbeAddOp2(v, OP_Rowid, iTab, iReg);
+      }else{
+        pIn->addrInTop = sqlite3VdbeAddOp3(v, OP_Column, iTab, 0, iReg);
+      }
+      pIn->eEndLoopOp = bRev ? OP_PrevIfOpen : OP_NextIfOpen;
+      sqlite3VdbeAddOp1(v, OP_IsNull, iReg); VdbeCoverage(v);
+    }else{
+      pLevel->u.in.nIn = 0;
+    }
+#endif
+  }
+  disableTerm(pLevel, pTerm);
+  return iReg;
+}
+
+/*
+** Generate code that will evaluate all == and IN constraints for an
+** index scan.
+**
+** For example, consider table t1(a,b,c,d,e,f) with index i1(a,b,c).
+** Suppose the WHERE clause is this:  a==5 AND b IN (1,2,3) AND c>5 AND c<10
+** The index has as many as three equality constraints, but in this
+** example, the third "c" value is an inequality.  So only two 
+** constraints are coded.  This routine will generate code to evaluate
+** a==5 and b IN (1,2,3).  The current values for a and b will be stored
+** in consecutive registers and the index of the first register is returned.
+**
+** In the example above nEq==2.  But this subroutine works for any value
+** of nEq including 0.  If nEq==0, this routine is nearly a no-op.
+** The only thing it does is allocate the pLevel->iMem memory cell and
+** compute the affinity string.
+**
+** The nExtraReg parameter is 0 or 1.  It is 0 if all WHERE clause constraints
+** are == or IN and are covered by the nEq.  nExtraReg is 1 if there is
+** an inequality constraint (such as the "c>=5 AND c<10" in the example) that
+** occurs after the nEq quality constraints.
+**
+** This routine allocates a range of nEq+nExtraReg memory cells and returns
+** the index of the first memory cell in that range. The code that
+** calls this routine will use that memory range to store keys for
+** start and termination conditions of the loop.
+** key value of the loop.  If one or more IN operators appear, then
+** this routine allocates an additional nEq memory cells for internal
+** use.
+**
+** Before returning, *pzAff is set to point to a buffer containing a
+** copy of the column affinity string of the index allocated using
+** sqlite3DbMalloc(). Except, entries in the copy of the string associated
+** with equality constraints that use NONE affinity are set to
+** SQLITE_AFF_NONE. This is to deal with SQL such as the following:
+**
+**   CREATE TABLE t1(a TEXT PRIMARY KEY, b);
+**   SELECT ... FROM t1 AS t2, t1 WHERE t1.a = t2.b;
+**
+** In the example above, the index on t1(a) has TEXT affinity. But since
+** the right hand side of the equality constraint (t2.b) has NONE affinity,
+** no conversion should be attempted before using a t2.b value as part of
+** a key to search the index. Hence the first byte in the returned affinity
+** string in this example would be set to SQLITE_AFF_NONE.
+*/
+static int codeAllEqualityTerms(
+  Parse *pParse,        /* Parsing context */
+  WhereLevel *pLevel,   /* Which nested loop of the FROM we are coding */
+  int bRev,             /* Reverse the order of IN operators */
+  int nExtraReg,        /* Number of extra registers to allocate */
+  char **pzAff          /* OUT: Set to point to affinity string */
+){
+  u16 nEq;                      /* The number of == or IN constraints to code */
+  u16 nSkip;                    /* Number of left-most columns to skip */
+  Vdbe *v = pParse->pVdbe;      /* The vm under construction */
+  Index *pIdx;                  /* The index being used for this loop */
+  WhereTerm *pTerm;             /* A single constraint term */
+  WhereLoop *pLoop;             /* The WhereLoop object */
+  int j;                        /* Loop counter */
+  int regBase;                  /* Base register */
+  int nReg;                     /* Number of registers to allocate */
+  char *zAff;                   /* Affinity string to return */
+
+  /* This module is only called on query plans that use an index. */
+  pLoop = pLevel->pWLoop;
+  assert( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0 );
+  nEq = pLoop->u.btree.nEq;
+  nSkip = pLoop->u.btree.nSkip;
+  pIdx = pLoop->u.btree.pIndex;
+  assert( pIdx!=0 );
+
+  /* Figure out how many memory cells we will need then allocate them.
+  */
+  regBase = pParse->nMem + 1;
+  nReg = pLoop->u.btree.nEq + nExtraReg;
+  pParse->nMem += nReg;
+
+  zAff = sqlite3DbStrDup(pParse->db, sqlite3IndexAffinityStr(v, pIdx));
+  if( !zAff ){
+    pParse->db->mallocFailed = 1;
+  }
+
+  if( nSkip ){
+    int iIdxCur = pLevel->iIdxCur;
+    sqlite3VdbeAddOp1(v, (bRev?OP_Last:OP_Rewind), iIdxCur);
+    VdbeCoverageIf(v, bRev==0);
+    VdbeCoverageIf(v, bRev!=0);
+    VdbeComment((v, "begin skip-scan on %s", pIdx->zName));
+    j = sqlite3VdbeAddOp0(v, OP_Goto);
+    pLevel->addrSkip = sqlite3VdbeAddOp4Int(v, (bRev?OP_SeekLT:OP_SeekGT),
+                            iIdxCur, 0, regBase, nSkip);
+    VdbeCoverageIf(v, bRev==0);
+    VdbeCoverageIf(v, bRev!=0);
+    sqlite3VdbeJumpHere(v, j);
+    for(j=0; j<nSkip; j++){
+      sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, j, regBase+j);
+      assert( pIdx->aiColumn[j]>=0 );
+      VdbeComment((v, "%s", pIdx->pTable->aCol[pIdx->aiColumn[j]].zName));
+    }
+  }    
+
+  /* Evaluate the equality constraints
+  */
+  assert( zAff==0 || (int)strlen(zAff)>=nEq );
+  for(j=nSkip; j<nEq; j++){
+    int r1;
+    pTerm = pLoop->aLTerm[j];
+    assert( pTerm!=0 );
+    /* The following testcase is true for indices with redundant columns. 
+    ** Ex: CREATE INDEX i1 ON t1(a,b,a); SELECT * FROM t1 WHERE a=0 AND b=0; */
+    testcase( (pTerm->wtFlags & TERM_CODED)!=0 );
+    testcase( pTerm->wtFlags & TERM_VIRTUAL );
+    r1 = codeEqualityTerm(pParse, pTerm, pLevel, j, bRev, regBase+j);
+    if( r1!=regBase+j ){
+      if( nReg==1 ){
+        sqlite3ReleaseTempReg(pParse, regBase);
+        regBase = r1;
+      }else{
+        sqlite3VdbeAddOp2(v, OP_SCopy, r1, regBase+j);
+      }
+    }
+    testcase( pTerm->eOperator & WO_ISNULL );
+    testcase( pTerm->eOperator & WO_IN );
+    if( (pTerm->eOperator & (WO_ISNULL|WO_IN))==0 ){
+      Expr *pRight = pTerm->pExpr->pRight;
+      if( sqlite3ExprCanBeNull(pRight) ){
+        sqlite3VdbeAddOp2(v, OP_IsNull, regBase+j, pLevel->addrBrk);
+        VdbeCoverage(v);
+      }
+      if( zAff ){
+        if( sqlite3CompareAffinity(pRight, zAff[j])==SQLITE_AFF_NONE ){
+          zAff[j] = SQLITE_AFF_NONE;
+        }
+        if( sqlite3ExprNeedsNoAffinityChange(pRight, zAff[j]) ){
+          zAff[j] = SQLITE_AFF_NONE;
+        }
+      }
+    }
+  }
+  *pzAff = zAff;
+  return regBase;
+}
+
+#ifndef SQLITE_OMIT_EXPLAIN
+/*
+** This routine is a helper for explainIndexRange() below
+**
+** pStr holds the text of an expression that we are building up one term
+** at a time.  This routine adds a new term to the end of the expression.
+** Terms are separated by AND so add the "AND" text for second and subsequent
+** terms only.
+*/
+static void explainAppendTerm(
+  StrAccum *pStr,             /* The text expression being built */
+  int iTerm,                  /* Index of this term.  First is zero */
+  const char *zColumn,        /* Name of the column */
+  const char *zOp             /* Name of the operator */
+){
+  if( iTerm ) sqlite3StrAccumAppend(pStr, " AND ", 5);
+  sqlite3StrAccumAppendAll(pStr, zColumn);
+  sqlite3StrAccumAppend(pStr, zOp, 1);
+  sqlite3StrAccumAppend(pStr, "?", 1);
+}
+
+/*
+** Argument pLevel describes a strategy for scanning table pTab. This 
+** function appends text to pStr that describes the subset of table
+** rows scanned by the strategy in the form of an SQL expression.
+**
+** For example, if the query:
+**
+**   SELECT * FROM t1 WHERE a=1 AND b>2;
+**
+** is run and there is an index on (a, b), then this function returns a
+** string similar to:
+**
+**   "a=? AND b>?"
+*/
+static void explainIndexRange(StrAccum *pStr, WhereLoop *pLoop, Table *pTab){
+  Index *pIndex = pLoop->u.btree.pIndex;
+  u16 nEq = pLoop->u.btree.nEq;
+  u16 nSkip = pLoop->u.btree.nSkip;
+  int i, j;
+  Column *aCol = pTab->aCol;
+  i16 *aiColumn = pIndex->aiColumn;
+
+  if( nEq==0 && (pLoop->wsFlags&(WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))==0 ) return;
+  sqlite3StrAccumAppend(pStr, " (", 2);
+  for(i=0; i<nEq; i++){
+    char *z = aiColumn[i] < 0 ? "rowid" : aCol[aiColumn[i]].zName;
+    if( i>=nSkip ){
+      explainAppendTerm(pStr, i, z, "=");
+    }else{
+      if( i ) sqlite3StrAccumAppend(pStr, " AND ", 5);
+      sqlite3XPrintf(pStr, 0, "ANY(%s)", z);
+    }
+  }
+
+  j = i;
+  if( pLoop->wsFlags&WHERE_BTM_LIMIT ){
+    char *z = aiColumn[j] < 0 ? "rowid" : aCol[aiColumn[j]].zName;
+    explainAppendTerm(pStr, i++, z, ">");
+  }
+  if( pLoop->wsFlags&WHERE_TOP_LIMIT ){
+    char *z = aiColumn[j] < 0 ? "rowid" : aCol[aiColumn[j]].zName;
+    explainAppendTerm(pStr, i, z, "<");
+  }
+  sqlite3StrAccumAppend(pStr, ")", 1);
+}
+
+/*
+** This function is a no-op unless currently processing an EXPLAIN QUERY PLAN
+** command. If the query being compiled is an EXPLAIN QUERY PLAN, a single
+** record is added to the output to describe the table scan strategy in 
+** pLevel.
+*/
+static void explainOneScan(
+  Parse *pParse,                  /* Parse context */
+  SrcList *pTabList,              /* Table list this loop refers to */
+  WhereLevel *pLevel,             /* Scan to write OP_Explain opcode for */
+  int iLevel,                     /* Value for "level" column of output */
+  int iFrom,                      /* Value for "from" column of output */
+  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */
+){
+#ifndef SQLITE_DEBUG
+  if( pParse->explain==2 )
+#endif
+  {
+    struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];
+    Vdbe *v = pParse->pVdbe;      /* VM being constructed */
+    sqlite3 *db = pParse->db;     /* Database handle */
+    int iId = pParse->iSelectId;  /* Select id (left-most output column) */
+    int isSearch;                 /* True for a SEARCH. False for SCAN. */
+    WhereLoop *pLoop;             /* The controlling WhereLoop object */
+    u32 flags;                    /* Flags that describe this loop */
+    char *zMsg;                   /* Text to add to EQP output */
+    StrAccum str;                 /* EQP output string */
+    char zBuf[100];               /* Initial space for EQP output string */
+
+    pLoop = pLevel->pWLoop;
+    flags = pLoop->wsFlags;
+    if( (flags&WHERE_MULTI_OR) || (wctrlFlags&WHERE_ONETABLE_ONLY) ) return;
+
+    isSearch = (flags&(WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))!=0
+            || ((flags&WHERE_VIRTUALTABLE)==0 && (pLoop->u.btree.nEq>0))
+            || (wctrlFlags&(WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX));
+
+    sqlite3StrAccumInit(&str, zBuf, sizeof(zBuf), SQLITE_MAX_LENGTH);
+    str.db = db;
+    sqlite3StrAccumAppendAll(&str, isSearch ? "SEARCH" : "SCAN");
+    if( pItem->pSelect ){
+      sqlite3XPrintf(&str, 0, " SUBQUERY %d", pItem->iSelectId);
+    }else{
+      sqlite3XPrintf(&str, 0, " TABLE %s", pItem->zName);
+    }
+
+    if( pItem->zAlias ){
+      sqlite3XPrintf(&str, 0, " AS %s", pItem->zAlias);
+    }
+    if( (flags & (WHERE_IPK|WHERE_VIRTUALTABLE))==0 ){
+      const char *zFmt = 0;
+      Index *pIdx;
+
+      assert( pLoop->u.btree.pIndex!=0 );
+      pIdx = pLoop->u.btree.pIndex;
+      assert( !(flags&WHERE_AUTO_INDEX) || (flags&WHERE_IDX_ONLY) );
+      if( !HasRowid(pItem->pTab) && IsPrimaryKeyIndex(pIdx) ){
+        if( isSearch ){
+          zFmt = "PRIMARY KEY";
+        }
+      }else if( flags & WHERE_AUTO_INDEX ){
+        zFmt = "AUTOMATIC COVERING INDEX";
+      }else if( flags & WHERE_IDX_ONLY ){
+        zFmt = "COVERING INDEX %s";
+      }else{
+        zFmt = "INDEX %s";
+      }
+      if( zFmt ){
+        sqlite3StrAccumAppend(&str, " USING ", 7);
+        sqlite3XPrintf(&str, 0, zFmt, pIdx->zName);
+        explainIndexRange(&str, pLoop, pItem->pTab);
+      }
+    }else if( (flags & WHERE_IPK)!=0 && (flags & WHERE_CONSTRAINT)!=0 ){
+      const char *zRange;
+      if( flags&(WHERE_COLUMN_EQ|WHERE_COLUMN_IN) ){
+        zRange = "(rowid=?)";
+      }else if( (flags&WHERE_BOTH_LIMIT)==WHERE_BOTH_LIMIT ){
+        zRange = "(rowid>? AND rowid<?)";
+      }else if( flags&WHERE_BTM_LIMIT ){
+        zRange = "(rowid>?)";
+      }else{
+        assert( flags&WHERE_TOP_LIMIT);
+        zRange = "(rowid<?)";
+      }
+      sqlite3StrAccumAppendAll(&str, " USING INTEGER PRIMARY KEY ");
+      sqlite3StrAccumAppendAll(&str, zRange);
+    }
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+    else if( (flags & WHERE_VIRTUALTABLE)!=0 ){
+      sqlite3XPrintf(&str, 0, " VIRTUAL TABLE INDEX %d:%s",
+                  pLoop->u.vtab.idxNum, pLoop->u.vtab.idxStr);
+    }
+#endif
+#ifdef SQLITE_EXPLAIN_ESTIMATED_ROWS
+    if( pLoop->nOut>=10 ){
+      sqlite3XPrintf(&str, 0, " (~%llu rows)", sqlite3LogEstToInt(pLoop->nOut));
+    }else{
+      sqlite3StrAccumAppend(&str, " (~1 row)", 9);
+    }
+#endif
+    zMsg = sqlite3StrAccumFinish(&str);
+    sqlite3VdbeAddOp4(v, OP_Explain, iId, iLevel, iFrom, zMsg, P4_DYNAMIC);
+  }
+}
+#else
+# define explainOneScan(u,v,w,x,y,z)
+#endif /* SQLITE_OMIT_EXPLAIN */
+
+
+/*
+** Generate code for the start of the iLevel-th loop in the WHERE clause
+** implementation described by pWInfo.
+*/
+static Bitmask codeOneLoopStart(
+  WhereInfo *pWInfo,   /* Complete information about the WHERE clause */
+  int iLevel,          /* Which level of pWInfo->a[] should be coded */
+  Bitmask notReady     /* Which tables are currently available */
+){
+  int j, k;            /* Loop counters */
+  int iCur;            /* The VDBE cursor for the table */
+  int addrNxt;         /* Where to jump to continue with the next IN case */
+  int omitTable;       /* True if we use the index only */
+  int bRev;            /* True if we need to scan in reverse order */
+  WhereLevel *pLevel;  /* The where level to be coded */
+  WhereLoop *pLoop;    /* The WhereLoop object being coded */
+  WhereClause *pWC;    /* Decomposition of the entire WHERE clause */
+  WhereTerm *pTerm;               /* A WHERE clause term */
+  Parse *pParse;                  /* Parsing context */
+  sqlite3 *db;                    /* Database connection */
+  Vdbe *v;                        /* The prepared stmt under constructions */
+  struct SrcList_item *pTabItem;  /* FROM clause term being coded */
+  int addrBrk;                    /* Jump here to break out of the loop */
+  int addrCont;                   /* Jump here to continue with next cycle */
+  int iRowidReg = 0;        /* Rowid is stored in this register, if not zero */
+  int iReleaseReg = 0;      /* Temp register to free before returning */
+
+  pParse = pWInfo->pParse;
+  v = pParse->pVdbe;
+  pWC = &pWInfo->sWC;
+  db = pParse->db;
+  pLevel = &pWInfo->a[iLevel];
+  pLoop = pLevel->pWLoop;
+  pTabItem = &pWInfo->pTabList->a[pLevel->iFrom];
+  iCur = pTabItem->iCursor;
+  pLevel->notReady = notReady & ~getMask(&pWInfo->sMaskSet, iCur);
+  bRev = (pWInfo->revMask>>iLevel)&1;
+  omitTable = (pLoop->wsFlags & WHERE_IDX_ONLY)!=0 
+           && (pWInfo->wctrlFlags & WHERE_FORCE_TABLE)==0;
+  VdbeModuleComment((v, "Begin WHERE-loop%d: %s",iLevel,pTabItem->pTab->zName));
+
+  /* Create labels for the "break" and "continue" instructions
+  ** for the current loop.  Jump to addrBrk to break out of a loop.
+  ** Jump to cont to go immediately to the next iteration of the
+  ** loop.
+  **
+  ** When there is an IN operator, we also have a "addrNxt" label that
+  ** means to continue with the next IN value combination.  When
+  ** there are no IN operators in the constraints, the "addrNxt" label
+  ** is the same as "addrBrk".
+  */
+  addrBrk = pLevel->addrBrk = pLevel->addrNxt = sqlite3VdbeMakeLabel(v);
+  addrCont = pLevel->addrCont = sqlite3VdbeMakeLabel(v);
+
+  /* If this is the right table of a LEFT OUTER JOIN, allocate and
+  ** initialize a memory cell that records if this table matches any
+  ** row of the left table of the join.
+  */
+  if( pLevel->iFrom>0 && (pTabItem[0].jointype & JT_LEFT)!=0 ){
+    pLevel->iLeftJoin = ++pParse->nMem;
+    sqlite3VdbeAddOp2(v, OP_Integer, 0, pLevel->iLeftJoin);
+    VdbeComment((v, "init LEFT JOIN no-match flag"));
+  }
+
+  /* Special case of a FROM clause subquery implemented as a co-routine */
+  if( pTabItem->viaCoroutine ){
+    int regYield = pTabItem->regReturn;
+    sqlite3VdbeAddOp3(v, OP_InitCoroutine, regYield, 0, pTabItem->addrFillSub);
+    pLevel->p2 =  sqlite3VdbeAddOp2(v, OP_Yield, regYield, addrBrk);
+    VdbeCoverage(v);
+    VdbeComment((v, "next row of \"%s\"", pTabItem->pTab->zName));
+    pLevel->op = OP_Goto;
+  }else
+
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+  if(  (pLoop->wsFlags & WHERE_VIRTUALTABLE)!=0 ){
+    /* Case 1:  The table is a virtual-table.  Use the VFilter and VNext
+    **          to access the data.
+    */
+    int iReg;   /* P3 Value for OP_VFilter */
+    int addrNotFound;
+    int nConstraint = pLoop->nLTerm;
+
+    sqlite3ExprCachePush(pParse);
+    iReg = sqlite3GetTempRange(pParse, nConstraint+2);
+    addrNotFound = pLevel->addrBrk;
+    for(j=0; j<nConstraint; j++){
+      int iTarget = iReg+j+2;
+      pTerm = pLoop->aLTerm[j];
+      if( pTerm==0 ) continue;
+      if( pTerm->eOperator & WO_IN ){
+        codeEqualityTerm(pParse, pTerm, pLevel, j, bRev, iTarget);
+        addrNotFound = pLevel->addrNxt;
+      }else{
+        sqlite3ExprCode(pParse, pTerm->pExpr->pRight, iTarget);
+      }
+    }
+    sqlite3VdbeAddOp2(v, OP_Integer, pLoop->u.vtab.idxNum, iReg);
+    sqlite3VdbeAddOp2(v, OP_Integer, nConstraint, iReg+1);
+    sqlite3VdbeAddOp4(v, OP_VFilter, iCur, addrNotFound, iReg,
+                      pLoop->u.vtab.idxStr,
+                      pLoop->u.vtab.needFree ? P4_MPRINTF : P4_STATIC);
+    VdbeCoverage(v);
+    pLoop->u.vtab.needFree = 0;
+    for(j=0; j<nConstraint && j<16; j++){
+      if( (pLoop->u.vtab.omitMask>>j)&1 ){
+        disableTerm(pLevel, pLoop->aLTerm[j]);
+      }
+    }
+    pLevel->op = OP_VNext;
+    pLevel->p1 = iCur;
+    pLevel->p2 = sqlite3VdbeCurrentAddr(v);
+    sqlite3ReleaseTempRange(pParse, iReg, nConstraint+2);
+    sqlite3ExprCachePop(pParse);
+  }else
+#endif /* SQLITE_OMIT_VIRTUALTABLE */
+
+  if( (pLoop->wsFlags & WHERE_IPK)!=0
+   && (pLoop->wsFlags & (WHERE_COLUMN_IN|WHERE_COLUMN_EQ))!=0
+  ){
+    /* Case 2:  We can directly reference a single row using an
+    **          equality comparison against the ROWID field.  Or
+    **          we reference multiple rows using a "rowid IN (...)"
+    **          construct.
+    */
+    assert( pLoop->u.btree.nEq==1 );
+    pTerm = pLoop->aLTerm[0];
+    assert( pTerm!=0 );
+    assert( pTerm->pExpr!=0 );
+    assert( omitTable==0 );
+    testcase( pTerm->wtFlags & TERM_VIRTUAL );
+    iReleaseReg = ++pParse->nMem;
+    iRowidReg = codeEqualityTerm(pParse, pTerm, pLevel, 0, bRev, iReleaseReg);
+    if( iRowidReg!=iReleaseReg ) sqlite3ReleaseTempReg(pParse, iReleaseReg);
+    addrNxt = pLevel->addrNxt;
+    sqlite3VdbeAddOp2(v, OP_MustBeInt, iRowidReg, addrNxt); VdbeCoverage(v);
+    sqlite3VdbeAddOp3(v, OP_NotExists, iCur, addrNxt, iRowidReg);
+    VdbeCoverage(v);
+    sqlite3ExprCacheAffinityChange(pParse, iRowidReg, 1);
+    sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
+    VdbeComment((v, "pk"));
+    pLevel->op = OP_Noop;
+  }else if( (pLoop->wsFlags & WHERE_IPK)!=0
+         && (pLoop->wsFlags & WHERE_COLUMN_RANGE)!=0
+  ){
+    /* Case 3:  We have an inequality comparison against the ROWID field.
+    */
+    int testOp = OP_Noop;
+    int start;
+    int memEndValue = 0;
+    WhereTerm *pStart, *pEnd;
+
+    assert( omitTable==0 );
+    j = 0;
+    pStart = pEnd = 0;
+    if( pLoop->wsFlags & WHERE_BTM_LIMIT ) pStart = pLoop->aLTerm[j++];
+    if( pLoop->wsFlags & WHERE_TOP_LIMIT ) pEnd = pLoop->aLTerm[j++];
+    assert( pStart!=0 || pEnd!=0 );
+    if( bRev ){
+      pTerm = pStart;
+      pStart = pEnd;
+      pEnd = pTerm;
+    }
+    if( pStart ){
+      Expr *pX;             /* The expression that defines the start bound */
+      int r1, rTemp;        /* Registers for holding the start boundary */
+
+      /* The following constant maps TK_xx codes into corresponding 
+      ** seek opcodes.  It depends on a particular ordering of TK_xx
+      */
+      const u8 aMoveOp[] = {
+           /* TK_GT */  OP_SeekGT,
+           /* TK_LE */  OP_SeekLE,
+           /* TK_LT */  OP_SeekLT,
+           /* TK_GE */  OP_SeekGE
+      };
+      assert( TK_LE==TK_GT+1 );      /* Make sure the ordering.. */
+      assert( TK_LT==TK_GT+2 );      /*  ... of the TK_xx values... */
+      assert( TK_GE==TK_GT+3 );      /*  ... is correcct. */
+
+      assert( (pStart->wtFlags & TERM_VNULL)==0 );
+      testcase( pStart->wtFlags & TERM_VIRTUAL );
+      pX = pStart->pExpr;
+      assert( pX!=0 );
+      testcase( pStart->leftCursor!=iCur ); /* transitive constraints */
+      r1 = sqlite3ExprCodeTemp(pParse, pX->pRight, &rTemp);
+      sqlite3VdbeAddOp3(v, aMoveOp[pX->op-TK_GT], iCur, addrBrk, r1);
+      VdbeComment((v, "pk"));
+      VdbeCoverageIf(v, pX->op==TK_GT);
+      VdbeCoverageIf(v, pX->op==TK_LE);
+      VdbeCoverageIf(v, pX->op==TK_LT);
+      VdbeCoverageIf(v, pX->op==TK_GE);
+      sqlite3ExprCacheAffinityChange(pParse, r1, 1);
+      sqlite3ReleaseTempReg(pParse, rTemp);
+      disableTerm(pLevel, pStart);
+    }else{
+      sqlite3VdbeAddOp2(v, bRev ? OP_Last : OP_Rewind, iCur, addrBrk);
+      VdbeCoverageIf(v, bRev==0);
+      VdbeCoverageIf(v, bRev!=0);
+    }
+    if( pEnd ){
+      Expr *pX;
+      pX = pEnd->pExpr;
+      assert( pX!=0 );
+      assert( (pEnd->wtFlags & TERM_VNULL)==0 );
+      testcase( pEnd->leftCursor!=iCur ); /* Transitive constraints */
+      testcase( pEnd->wtFlags & TERM_VIRTUAL );
+      memEndValue = ++pParse->nMem;
+      sqlite3ExprCode(pParse, pX->pRight, memEndValue);
+      if( pX->op==TK_LT || pX->op==TK_GT ){
+        testOp = bRev ? OP_Le : OP_Ge;
+      }else{
+        testOp = bRev ? OP_Lt : OP_Gt;
+      }
+      disableTerm(pLevel, pEnd);
+    }
+    start = sqlite3VdbeCurrentAddr(v);
+    pLevel->op = bRev ? OP_Prev : OP_Next;
+    pLevel->p1 = iCur;
+    pLevel->p2 = start;
+    assert( pLevel->p5==0 );
+    if( testOp!=OP_Noop ){
+      iRowidReg = ++pParse->nMem;
+      sqlite3VdbeAddOp2(v, OP_Rowid, iCur, iRowidReg);
+      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
+      sqlite3VdbeAddOp3(v, testOp, memEndValue, addrBrk, iRowidReg);
+      VdbeCoverageIf(v, testOp==OP_Le);
+      VdbeCoverageIf(v, testOp==OP_Lt);
+      VdbeCoverageIf(v, testOp==OP_Ge);
+      VdbeCoverageIf(v, testOp==OP_Gt);
+      sqlite3VdbeChangeP5(v, SQLITE_AFF_NUMERIC | SQLITE_JUMPIFNULL);
+    }
+  }else if( pLoop->wsFlags & WHERE_INDEXED ){
+    /* Case 4: A scan using an index.
+    **
+    **         The WHERE clause may contain zero or more equality 
+    **         terms ("==" or "IN" operators) that refer to the N
+    **         left-most columns of the index. It may also contain
+    **         inequality constraints (>, <, >= or <=) on the indexed
+    **         column that immediately follows the N equalities. Only 
+    **         the right-most column can be an inequality - the rest must
+    **         use the "==" and "IN" operators. For example, if the 
+    **         index is on (x,y,z), then the following clauses are all 
+    **         optimized:
+    **
+    **            x=5
+    **            x=5 AND y=10
+    **            x=5 AND y<10
+    **            x=5 AND y>5 AND y<10
+    **            x=5 AND y=5 AND z<=10
+    **
+    **         The z<10 term of the following cannot be used, only
+    **         the x=5 term:
+    **
+    **            x=5 AND z<10
+    **
+    **         N may be zero if there are inequality constraints.
+    **         If there are no inequality constraints, then N is at
+    **         least one.
+    **
+    **         This case is also used when there are no WHERE clause
+    **         constraints but an index is selected anyway, in order
+    **         to force the output order to conform to an ORDER BY.
+    */  
+    static const u8 aStartOp[] = {
+      0,
+      0,
+      OP_Rewind,           /* 2: (!start_constraints && startEq &&  !bRev) */
+      OP_Last,             /* 3: (!start_constraints && startEq &&   bRev) */
+      OP_SeekGT,           /* 4: (start_constraints  && !startEq && !bRev) */
+      OP_SeekLT,           /* 5: (start_constraints  && !startEq &&  bRev) */
+      OP_SeekGE,           /* 6: (start_constraints  &&  startEq && !bRev) */
+      OP_SeekLE            /* 7: (start_constraints  &&  startEq &&  bRev) */
+    };
+    static const u8 aEndOp[] = {
+      OP_IdxGE,            /* 0: (end_constraints && !bRev && !endEq) */
+      OP_IdxGT,            /* 1: (end_constraints && !bRev &&  endEq) */
+      OP_IdxLE,            /* 2: (end_constraints &&  bRev && !endEq) */
+      OP_IdxLT,            /* 3: (end_constraints &&  bRev &&  endEq) */
+    };
+    u16 nEq = pLoop->u.btree.nEq;     /* Number of == or IN terms */
+    int regBase;                 /* Base register holding constraint values */
+    WhereTerm *pRangeStart = 0;  /* Inequality constraint at range start */
+    WhereTerm *pRangeEnd = 0;    /* Inequality constraint at range end */
+    int startEq;                 /* True if range start uses ==, >= or <= */
+    int endEq;                   /* True if range end uses ==, >= or <= */
+    int start_constraints;       /* Start of range is constrained */
+    int nConstraint;             /* Number of constraint terms */
+    Index *pIdx;                 /* The index we will be using */
+    int iIdxCur;                 /* The VDBE cursor for the index */
+    int nExtraReg = 0;           /* Number of extra registers needed */
+    int op;                      /* Instruction opcode */
+    char *zStartAff;             /* Affinity for start of range constraint */
+    char cEndAff = 0;            /* Affinity for end of range constraint */
+    u8 bSeekPastNull = 0;        /* True to seek past initial nulls */
+    u8 bStopAtNull = 0;          /* Add condition to terminate at NULLs */
+
+    pIdx = pLoop->u.btree.pIndex;
+    iIdxCur = pLevel->iIdxCur;
+    assert( nEq>=pLoop->u.btree.nSkip );
+
+    /* If this loop satisfies a sort order (pOrderBy) request that 
+    ** was passed to this function to implement a "SELECT min(x) ..." 
+    ** query, then the caller will only allow the loop to run for
+    ** a single iteration. This means that the first row returned
+    ** should not have a NULL value stored in 'x'. If column 'x' is
+    ** the first one after the nEq equality constraints in the index,
+    ** this requires some special handling.
+    */
+    assert( pWInfo->pOrderBy==0
+         || pWInfo->pOrderBy->nExpr==1
+         || (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)==0 );
+    if( (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)!=0
+     && pWInfo->nOBSat>0
+     && (pIdx->nKeyCol>nEq)
+    ){
+      assert( pLoop->u.btree.nSkip==0 );
+      bSeekPastNull = 1;
+      nExtraReg = 1;
+    }
+
+    /* Find any inequality constraint terms for the start and end 
+    ** of the range. 
+    */
+    j = nEq;
+    if( pLoop->wsFlags & WHERE_BTM_LIMIT ){
+      pRangeStart = pLoop->aLTerm[j++];
+      nExtraReg = 1;
+    }
+    if( pLoop->wsFlags & WHERE_TOP_LIMIT ){
+      pRangeEnd = pLoop->aLTerm[j++];
+      nExtraReg = 1;
+      if( pRangeStart==0
+       && (j = pIdx->aiColumn[nEq])>=0 
+       && pIdx->pTable->aCol[j].notNull==0
+      ){
+        bSeekPastNull = 1;
+      }
+    }
+    assert( pRangeEnd==0 || (pRangeEnd->wtFlags & TERM_VNULL)==0 );
+
+    /* Generate code to evaluate all constraint terms using == or IN
+    ** and store the values of those terms in an array of registers
+    ** starting at regBase.
+    */
+    regBase = codeAllEqualityTerms(pParse,pLevel,bRev,nExtraReg,&zStartAff);
+    assert( zStartAff==0 || sqlite3Strlen30(zStartAff)>=nEq );
+    if( zStartAff ) cEndAff = zStartAff[nEq];
+    addrNxt = pLevel->addrNxt;
+
+    /* If we are doing a reverse order scan on an ascending index, or
+    ** a forward order scan on a descending index, interchange the 
+    ** start and end terms (pRangeStart and pRangeEnd).
+    */
+    if( (nEq<pIdx->nKeyCol && bRev==(pIdx->aSortOrder[nEq]==SQLITE_SO_ASC))
+     || (bRev && pIdx->nKeyCol==nEq)
+    ){
+      SWAP(WhereTerm *, pRangeEnd, pRangeStart);
+      SWAP(u8, bSeekPastNull, bStopAtNull);
+    }
+
+    testcase( pRangeStart && (pRangeStart->eOperator & WO_LE)!=0 );
+    testcase( pRangeStart && (pRangeStart->eOperator & WO_GE)!=0 );
+    testcase( pRangeEnd && (pRangeEnd->eOperator & WO_LE)!=0 );
+    testcase( pRangeEnd && (pRangeEnd->eOperator & WO_GE)!=0 );
+    startEq = !pRangeStart || pRangeStart->eOperator & (WO_LE|WO_GE);
+    endEq =   !pRangeEnd || pRangeEnd->eOperator & (WO_LE|WO_GE);
+    start_constraints = pRangeStart || nEq>0;
+
+    /* Seek the index cursor to the start of the range. */
+    nConstraint = nEq;
+    if( pRangeStart ){
+      Expr *pRight = pRangeStart->pExpr->pRight;
+      sqlite3ExprCode(pParse, pRight, regBase+nEq);
+      if( (pRangeStart->wtFlags & TERM_VNULL)==0
+       && sqlite3ExprCanBeNull(pRight)
+      ){
+        sqlite3VdbeAddOp2(v, OP_IsNull, regBase+nEq, addrNxt);
+        VdbeCoverage(v);
+      }
+      if( zStartAff ){
+        if( sqlite3CompareAffinity(pRight, zStartAff[nEq])==SQLITE_AFF_NONE){
+          /* Since the comparison is to be performed with no conversions
+          ** applied to the operands, set the affinity to apply to pRight to 
+          ** SQLITE_AFF_NONE.  */
+          zStartAff[nEq] = SQLITE_AFF_NONE;
+        }
+        if( sqlite3ExprNeedsNoAffinityChange(pRight, zStartAff[nEq]) ){
+          zStartAff[nEq] = SQLITE_AFF_NONE;
+        }
+      }  
+      nConstraint++;
+      testcase( pRangeStart->wtFlags & TERM_VIRTUAL );
+    }else if( bSeekPastNull ){
+      sqlite3VdbeAddOp2(v, OP_Null, 0, regBase+nEq);
+      nConstraint++;
+      startEq = 0;
+      start_constraints = 1;
+    }
+    codeApplyAffinity(pParse, regBase, nConstraint - bSeekPastNull, zStartAff);
+    op = aStartOp[(start_constraints<<2) + (startEq<<1) + bRev];
+    assert( op!=0 );
+    sqlite3VdbeAddOp4Int(v, op, iIdxCur, addrNxt, regBase, nConstraint);
+    VdbeCoverage(v);
+    VdbeCoverageIf(v, op==OP_Rewind);  testcase( op==OP_Rewind );
+    VdbeCoverageIf(v, op==OP_Last);    testcase( op==OP_Last );
+    VdbeCoverageIf(v, op==OP_SeekGT);  testcase( op==OP_SeekGT );
+    VdbeCoverageIf(v, op==OP_SeekGE);  testcase( op==OP_SeekGE );
+    VdbeCoverageIf(v, op==OP_SeekLE);  testcase( op==OP_SeekLE );
+    VdbeCoverageIf(v, op==OP_SeekLT);  testcase( op==OP_SeekLT );
+
+    /* Load the value for the inequality constraint at the end of the
+    ** range (if any).
+    */
+    nConstraint = nEq;
+    if( pRangeEnd ){
+      Expr *pRight = pRangeEnd->pExpr->pRight;
+      sqlite3ExprCacheRemove(pParse, regBase+nEq, 1);
+      sqlite3ExprCode(pParse, pRight, regBase+nEq);
+      if( (pRangeEnd->wtFlags & TERM_VNULL)==0
+       && sqlite3ExprCanBeNull(pRight)
+      ){
+        sqlite3VdbeAddOp2(v, OP_IsNull, regBase+nEq, addrNxt);
+        VdbeCoverage(v);
+      }
+      if( sqlite3CompareAffinity(pRight, cEndAff)!=SQLITE_AFF_NONE
+       && !sqlite3ExprNeedsNoAffinityChange(pRight, cEndAff)
+      ){
+        codeApplyAffinity(pParse, regBase+nEq, 1, &cEndAff);
+      }
+      nConstraint++;
+      testcase( pRangeEnd->wtFlags & TERM_VIRTUAL );
+    }else if( bStopAtNull ){
+      sqlite3VdbeAddOp2(v, OP_Null, 0, regBase+nEq);
+      endEq = 0;
+      nConstraint++;
+    }
+    sqlite3DbFree(db, zStartAff);
+
+    /* Top of the loop body */
+    pLevel->p2 = sqlite3VdbeCurrentAddr(v);
+
+    /* Check if the index cursor is past the end of the range. */
+    if( nConstraint ){
+      op = aEndOp[bRev*2 + endEq];
+      sqlite3VdbeAddOp4Int(v, op, iIdxCur, addrNxt, regBase, nConstraint);
+      testcase( op==OP_IdxGT );  VdbeCoverageIf(v, op==OP_IdxGT );
+      testcase( op==OP_IdxGE );  VdbeCoverageIf(v, op==OP_IdxGE );
+      testcase( op==OP_IdxLT );  VdbeCoverageIf(v, op==OP_IdxLT );
+      testcase( op==OP_IdxLE );  VdbeCoverageIf(v, op==OP_IdxLE );
+    }
+
+    /* Seek the table cursor, if required */
+    disableTerm(pLevel, pRangeStart);
+    disableTerm(pLevel, pRangeEnd);
+    if( omitTable ){
+      /* pIdx is a covering index.  No need to access the main table. */
+    }else if( HasRowid(pIdx->pTable) ){
+      iRowidReg = ++pParse->nMem;
+      sqlite3VdbeAddOp2(v, OP_IdxRowid, iIdxCur, iRowidReg);
+      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);
+      sqlite3VdbeAddOp2(v, OP_Seek, iCur, iRowidReg);  /* Deferred seek */
+    }else if( iCur!=iIdxCur ){
+      Index *pPk = sqlite3PrimaryKeyIndex(pIdx->pTable);
+      iRowidReg = sqlite3GetTempRange(pParse, pPk->nKeyCol);
+      for(j=0; j<pPk->nKeyCol; j++){
+        k = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[j]);
+        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, k, iRowidReg+j);
+      }
+      sqlite3VdbeAddOp4Int(v, OP_NotFound, iCur, addrCont,
+                           iRowidReg, pPk->nKeyCol); VdbeCoverage(v);
+    }
+
+    /* Record the instruction used to terminate the loop. Disable 
+    ** WHERE clause terms made redundant by the index range scan.
+    */
+    if( pLoop->wsFlags & WHERE_ONEROW ){
+      pLevel->op = OP_Noop;
+    }else if( bRev ){
+      pLevel->op = OP_Prev;
+    }else{
+      pLevel->op = OP_Next;
+    }
+    pLevel->p1 = iIdxCur;
+    pLevel->p3 = (pLoop->wsFlags&WHERE_UNQ_WANTED)!=0 ? 1:0;
+    if( (pLoop->wsFlags & WHERE_CONSTRAINT)==0 ){
+      pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;
+    }else{
+      assert( pLevel->p5==0 );
+    }
+  }else
+
+#ifndef SQLITE_OMIT_OR_OPTIMIZATION
+  if( pLoop->wsFlags & WHERE_MULTI_OR ){
+    /* Case 5:  Two or more separately indexed terms connected by OR
+    **
+    ** Example:
+    **
+    **   CREATE TABLE t1(a,b,c,d);
+    **   CREATE INDEX i1 ON t1(a);
+    **   CREATE INDEX i2 ON t1(b);
+    **   CREATE INDEX i3 ON t1(c);
+    **
+    **   SELECT * FROM t1 WHERE a=5 OR b=7 OR (c=11 AND d=13)
+    **
+    ** In the example, there are three indexed terms connected by OR.
+    ** The top of the loop looks like this:
+    **
+    **          Null       1                # Zero the rowset in reg 1
+    **
+    ** Then, for each indexed term, the following. The arguments to
+    ** RowSetTest are such that the rowid of the current row is inserted
+    ** into the RowSet. If it is already present, control skips the
+    ** Gosub opcode and jumps straight to the code generated by WhereEnd().
+    **
+    **        sqlite3WhereBegin(<term>)
+    **          RowSetTest                  # Insert rowid into rowset
+    **          Gosub      2 A
+    **        sqlite3WhereEnd()
+    **
+    ** Following the above, code to terminate the loop. Label A, the target
+    ** of the Gosub above, jumps to the instruction right after the Goto.
+    **
+    **          Null       1                # Zero the rowset in reg 1
+    **          Goto       B                # The loop is finished.
+    **
+    **       A: <loop body>                 # Return data, whatever.
+    **
+    **          Return     2                # Jump back to the Gosub
+    **
+    **       B: <after the loop>
+    **
+    ** Added 2014-05-26: If the table is a WITHOUT ROWID table, then
+    ** use an ephemeral index instead of a RowSet to record the primary
+    ** keys of the rows we have already seen.
+    **
+    */
+    WhereClause *pOrWc;    /* The OR-clause broken out into subterms */
+    SrcList *pOrTab;       /* Shortened table list or OR-clause generation */
+    Index *pCov = 0;             /* Potential covering index (or NULL) */
+    int iCovCur = pParse->nTab++;  /* Cursor used for index scans (if any) */
+
+    int regReturn = ++pParse->nMem;           /* Register used with OP_Gosub */
+    int regRowset = 0;                        /* Register for RowSet object */
+    int regRowid = 0;                         /* Register holding rowid */
+    int iLoopBody = sqlite3VdbeMakeLabel(v);  /* Start of loop body */
+    int iRetInit;                             /* Address of regReturn init */
+    int untestedTerms = 0;             /* Some terms not completely tested */
+    int ii;                            /* Loop counter */
+    u16 wctrlFlags;                    /* Flags for sub-WHERE clause */
+    Expr *pAndExpr = 0;                /* An ".. AND (...)" expression */
+    Table *pTab = pTabItem->pTab;
+   
+    pTerm = pLoop->aLTerm[0];
+    assert( pTerm!=0 );
+    assert( pTerm->eOperator & WO_OR );
+    assert( (pTerm->wtFlags & TERM_ORINFO)!=0 );
+    pOrWc = &pTerm->u.pOrInfo->wc;
+    pLevel->op = OP_Return;
+    pLevel->p1 = regReturn;
+
+    /* Set up a new SrcList in pOrTab containing the table being scanned
+    ** by this loop in the a[0] slot and all notReady tables in a[1..] slots.
+    ** This becomes the SrcList in the recursive call to sqlite3WhereBegin().
+    */
+    if( pWInfo->nLevel>1 ){
+      int nNotReady;                 /* The number of notReady tables */
+      struct SrcList_item *origSrc;     /* Original list of tables */
+      nNotReady = pWInfo->nLevel - iLevel - 1;
+      pOrTab = sqlite3StackAllocRaw(db,
+                            sizeof(*pOrTab)+ nNotReady*sizeof(pOrTab->a[0]));
+      if( pOrTab==0 ) return notReady;
+      pOrTab->nAlloc = (u8)(nNotReady + 1);
+      pOrTab->nSrc = pOrTab->nAlloc;
+      memcpy(pOrTab->a, pTabItem, sizeof(*pTabItem));
+      origSrc = pWInfo->pTabList->a;
+      for(k=1; k<=nNotReady; k++){
+        memcpy(&pOrTab->a[k], &origSrc[pLevel[k].iFrom], sizeof(pOrTab->a[k]));
+      }
+    }else{
+      pOrTab = pWInfo->pTabList;
+    }
+
+    /* Initialize the rowset register to contain NULL. An SQL NULL is 
+    ** equivalent to an empty rowset.  Or, create an ephemeral index
+    ** capable of holding primary keys in the case of a WITHOUT ROWID.
+    **
+    ** Also initialize regReturn to contain the address of the instruction 
+    ** immediately following the OP_Return at the bottom of the loop. This
+    ** is required in a few obscure LEFT JOIN cases where control jumps
+    ** over the top of the loop into the body of it. In this case the 
+    ** correct response for the end-of-loop code (the OP_Return) is to 
+    ** fall through to the next instruction, just as an OP_Next does if
+    ** called on an uninitialized cursor.
+    */
+    if( (pWInfo->wctrlFlags & WHERE_DUPLICATES_OK)==0 ){
+      if( HasRowid(pTab) ){
+        regRowset = ++pParse->nMem;
+        sqlite3VdbeAddOp2(v, OP_Null, 0, regRowset);
+      }else{
+        Index *pPk = sqlite3PrimaryKeyIndex(pTab);
+        regRowset = pParse->nTab++;
+        sqlite3VdbeAddOp2(v, OP_OpenEphemeral, regRowset, pPk->nKeyCol);
+        sqlite3VdbeSetP4KeyInfo(pParse, pPk);
+      }
+      regRowid = ++pParse->nMem;
+    }
+    iRetInit = sqlite3VdbeAddOp2(v, OP_Integer, 0, regReturn);
+
+    /* If the original WHERE clause is z of the form:  (x1 OR x2 OR ...) AND y
+    ** Then for every term xN, evaluate as the subexpression: xN AND z
+    ** That way, terms in y that are factored into the disjunction will
+    ** be picked up by the recursive calls to sqlite3WhereBegin() below.
+    **
+    ** Actually, each subexpression is converted to "xN AND w" where w is
+    ** the "interesting" terms of z - terms that did not originate in the
+    ** ON or USING clause of a LEFT JOIN, and terms that are usable as 
+    ** indices.
+    **
+    ** This optimization also only applies if the (x1 OR x2 OR ...) term
+    ** is not contained in the ON clause of a LEFT JOIN.
+    ** See ticket http://www.sqlite.org/src/info/f2369304e4
+    */
+    if( pWC->nTerm>1 ){
+      int iTerm;
+      for(iTerm=0; iTerm<pWC->nTerm; iTerm++){
+        Expr *pExpr = pWC->a[iTerm].pExpr;
+        if( &pWC->a[iTerm] == pTerm ) continue;
+        if( ExprHasProperty(pExpr, EP_FromJoin) ) continue;
+        testcase( pWC->a[iTerm].wtFlags & TERM_ORINFO );
+        testcase( pWC->a[iTerm].wtFlags & TERM_VIRTUAL );
+        if( pWC->a[iTerm].wtFlags & (TERM_ORINFO|TERM_VIRTUAL) ) continue;
+        if( (pWC->a[iTerm].eOperator & WO_ALL)==0 ) continue;
+        pExpr = sqlite3ExprDup(db, pExpr, 0);
+        pAndExpr = sqlite3ExprAnd(db, pAndExpr, pExpr);
+      }
+      if( pAndExpr ){
+        pAndExpr = sqlite3PExpr(pParse, TK_AND, 0, pAndExpr, 0);
+      }
+    }
+
+    /* Run a separate WHERE clause for each term of the OR clause.  After
+    ** eliminating duplicates from other WHERE clauses, the action for each
+    ** sub-WHERE clause is to to invoke the main loop body as a subroutine.
+    */
+    wctrlFlags =  WHERE_OMIT_OPEN_CLOSE
+                | WHERE_FORCE_TABLE
+                | WHERE_ONETABLE_ONLY;
+    for(ii=0; ii<pOrWc->nTerm; ii++){
+      WhereTerm *pOrTerm = &pOrWc->a[ii];
+      if( pOrTerm->leftCursor==iCur || (pOrTerm->eOperator & WO_AND)!=0 ){
+        WhereInfo *pSubWInfo;           /* Info for single OR-term scan */
+        Expr *pOrExpr = pOrTerm->pExpr; /* Current OR clause term */
+        int j1 = 0;                     /* Address of jump operation */
+        if( pAndExpr && !ExprHasProperty(pOrExpr, EP_FromJoin) ){
+          pAndExpr->pLeft = pOrExpr;
+          pOrExpr = pAndExpr;
+        }
+        /* Loop through table entries that match term pOrTerm. */
+        WHERETRACE(0xffff, ("Subplan for OR-clause:\n"));
+        pSubWInfo = sqlite3WhereBegin(pParse, pOrTab, pOrExpr, 0, 0,
+                                      wctrlFlags, iCovCur);
+        assert( pSubWInfo || pParse->nErr || db->mallocFailed );
+        if( pSubWInfo ){
+          WhereLoop *pSubLoop;
+          explainOneScan(
+              pParse, pOrTab, &pSubWInfo->a[0], iLevel, pLevel->iFrom, 0
+          );
+          /* This is the sub-WHERE clause body.  First skip over
+          ** duplicate rows from prior sub-WHERE clauses, and record the
+          ** rowid (or PRIMARY KEY) for the current row so that the same
+          ** row will be skipped in subsequent sub-WHERE clauses.
+          */
+          if( (pWInfo->wctrlFlags & WHERE_DUPLICATES_OK)==0 ){
+            int r;
+            int iSet = ((ii==pOrWc->nTerm-1)?-1:ii);
+            if( HasRowid(pTab) ){
+              r = sqlite3ExprCodeGetColumn(pParse, pTab, -1, iCur, regRowid, 0);
+              j1 = sqlite3VdbeAddOp4Int(v, OP_RowSetTest, regRowset, 0, r,iSet);
+              VdbeCoverage(v);
+            }else{
+              Index *pPk = sqlite3PrimaryKeyIndex(pTab);
+              int nPk = pPk->nKeyCol;
+              int iPk;
+
+              /* Read the PK into an array of temp registers. */
+              r = sqlite3GetTempRange(pParse, nPk);
+              for(iPk=0; iPk<nPk; iPk++){
+                int iCol = pPk->aiColumn[iPk];
+                sqlite3ExprCodeGetColumn(pParse, pTab, iCol, iCur, r+iPk, 0);
+              }
+
+              /* Check if the temp table already contains this key. If so,
+              ** the row has already been included in the result set and
+              ** can be ignored (by jumping past the Gosub below). Otherwise,
+              ** insert the key into the temp table and proceed with processing
+              ** the row.
+              **
+              ** Use some of the same optimizations as OP_RowSetTest: If iSet
+              ** is zero, assume that the key cannot already be present in
+              ** the temp table. And if iSet is -1, assume that there is no 
+              ** need to insert the key into the temp table, as it will never 
+              ** be tested for.  */ 
+              if( iSet ){
+                j1 = sqlite3VdbeAddOp4Int(v, OP_Found, regRowset, 0, r, nPk);
+                VdbeCoverage(v);
+              }
+              if( iSet>=0 ){
+                sqlite3VdbeAddOp3(v, OP_MakeRecord, r, nPk, regRowid);
+                sqlite3VdbeAddOp3(v, OP_IdxInsert, regRowset, regRowid, 0);
+                if( iSet ) sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);
+              }
+
+              /* Release the array of temp registers */
+              sqlite3ReleaseTempRange(pParse, r, nPk);
+            }
+          }
+
+          /* Invoke the main loop body as a subroutine */
+          sqlite3VdbeAddOp2(v, OP_Gosub, regReturn, iLoopBody);
+
+          /* Jump here (skipping the main loop body subroutine) if the
+          ** current sub-WHERE row is a duplicate from prior sub-WHEREs. */
+          if( j1 ) sqlite3VdbeJumpHere(v, j1);
+
+          /* The pSubWInfo->untestedTerms flag means that this OR term
+          ** contained one or more AND term from a notReady table.  The
+          ** terms from the notReady table could not be tested and will
+          ** need to be tested later.
+          */
+          if( pSubWInfo->untestedTerms ) untestedTerms = 1;
+
+          /* If all of the OR-connected terms are optimized using the same
+          ** index, and the index is opened using the same cursor number
+          ** by each call to sqlite3WhereBegin() made by this loop, it may
+          ** be possible to use that index as a covering index.
+          **
+          ** If the call to sqlite3WhereBegin() above resulted in a scan that
+          ** uses an index, and this is either the first OR-connected term
+          ** processed or the index is the same as that used by all previous
+          ** terms, set pCov to the candidate covering index. Otherwise, set 
+          ** pCov to NULL to indicate that no candidate covering index will 
+          ** be available.
+          */
+          pSubLoop = pSubWInfo->a[0].pWLoop;
+          assert( (pSubLoop->wsFlags & WHERE_AUTO_INDEX)==0 );
+          if( (pSubLoop->wsFlags & WHERE_INDEXED)!=0
+           && (ii==0 || pSubLoop->u.btree.pIndex==pCov)
+           && (HasRowid(pTab) || !IsPrimaryKeyIndex(pSubLoop->u.btree.pIndex))
+          ){
+            assert( pSubWInfo->a[0].iIdxCur==iCovCur );
+            pCov = pSubLoop->u.btree.pIndex;
+            wctrlFlags |= WHERE_REOPEN_IDX;
+          }else{
+            pCov = 0;
+          }
+
+          /* Finish the loop through table entries that match term pOrTerm. */
+          sqlite3WhereEnd(pSubWInfo);
+        }
+      }
+    }
+    pLevel->u.pCovidx = pCov;
+    if( pCov ) pLevel->iIdxCur = iCovCur;
+    if( pAndExpr ){
+      pAndExpr->pLeft = 0;
+      sqlite3ExprDelete(db, pAndExpr);
+    }
+    sqlite3VdbeChangeP1(v, iRetInit, sqlite3VdbeCurrentAddr(v));
+    sqlite3VdbeAddOp2(v, OP_Goto, 0, pLevel->addrBrk);
+    sqlite3VdbeResolveLabel(v, iLoopBody);
+
+    if( pWInfo->nLevel>1 ) sqlite3StackFree(db, pOrTab);
+    if( !untestedTerms ) disableTerm(pLevel, pTerm);
+  }else
+#endif /* SQLITE_OMIT_OR_OPTIMIZATION */
+
+  {
+    /* Case 6:  There is no usable index.  We must do a complete
+    **          scan of the entire table.
+    */
+    static const u8 aStep[] = { OP_Next, OP_Prev };
+    static const u8 aStart[] = { OP_Rewind, OP_Last };
+    assert( bRev==0 || bRev==1 );
+    if( pTabItem->isRecursive ){
+      /* Tables marked isRecursive have only a single row that is stored in
+      ** a pseudo-cursor.  No need to Rewind or Next such cursors. */
+      pLevel->op = OP_Noop;
+    }else{
+      pLevel->op = aStep[bRev];
+      pLevel->p1 = iCur;
+      pLevel->p2 = 1 + sqlite3VdbeAddOp2(v, aStart[bRev], iCur, addrBrk);
+      VdbeCoverageIf(v, bRev==0);
+      VdbeCoverageIf(v, bRev!=0);
+      pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;
+    }
+  }
+
+  /* Insert code to test every subexpression that can be completely
+  ** computed using the current set of tables.
+  */
+  for(pTerm=pWC->a, j=pWC->nTerm; j>0; j--, pTerm++){
+    Expr *pE;
+    testcase( pTerm->wtFlags & TERM_VIRTUAL );
+    testcase( pTerm->wtFlags & TERM_CODED );
+    if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;
+    if( (pTerm->prereqAll & pLevel->notReady)!=0 ){
+      testcase( pWInfo->untestedTerms==0
+               && (pWInfo->wctrlFlags & WHERE_ONETABLE_ONLY)!=0 );
+      pWInfo->untestedTerms = 1;
+      continue;
+    }
+    pE = pTerm->pExpr;
+    assert( pE!=0 );
+    if( pLevel->iLeftJoin && !ExprHasProperty(pE, EP_FromJoin) ){
+      continue;
+    }
+    sqlite3ExprIfFalse(pParse, pE, addrCont, SQLITE_JUMPIFNULL);
+    pTerm->wtFlags |= TERM_CODED;
+  }
+
+  /* Insert code to test for implied constraints based on transitivity
+  ** of the "==" operator.
+  **
+  ** Example: If the WHERE clause contains "t1.a=t2.b" and "t2.b=123"
+  ** and we are coding the t1 loop and the t2 loop has not yet coded,
+  ** then we cannot use the "t1.a=t2.b" constraint, but we can code
+  ** the implied "t1.a=123" constraint.
+  */
+  for(pTerm=pWC->a, j=pWC->nTerm; j>0; j--, pTerm++){
+    Expr *pE, *pEAlt;
+    WhereTerm *pAlt;
+    if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;
+    if( pTerm->eOperator!=(WO_EQUIV|WO_EQ) ) continue;
+    if( pTerm->leftCursor!=iCur ) continue;
+    if( pLevel->iLeftJoin ) continue;
+    pE = pTerm->pExpr;
+    assert( !ExprHasProperty(pE, EP_FromJoin) );
+    assert( (pTerm->prereqRight & pLevel->notReady)!=0 );
+    pAlt = findTerm(pWC, iCur, pTerm->u.leftColumn, notReady, WO_EQ|WO_IN, 0);
+    if( pAlt==0 ) continue;
+    if( pAlt->wtFlags & (TERM_CODED) ) continue;
+    testcase( pAlt->eOperator & WO_EQ );
+    testcase( pAlt->eOperator & WO_IN );
+    VdbeModuleComment((v, "begin transitive constraint"));
+    pEAlt = sqlite3StackAllocRaw(db, sizeof(*pEAlt));
+    if( pEAlt ){
+      *pEAlt = *pAlt->pExpr;
+      pEAlt->pLeft = pE->pLeft;
+      sqlite3ExprIfFalse(pParse, pEAlt, addrCont, SQLITE_JUMPIFNULL);
+      sqlite3StackFree(db, pEAlt);
+    }
+  }
+
+  /* For a LEFT OUTER JOIN, generate code that will record the fact that
+  ** at least one row of the right table has matched the left table.  
+  */
+  if( pLevel->iLeftJoin ){
+    pLevel->addrFirst = sqlite3VdbeCurrentAddr(v);
+    sqlite3VdbeAddOp2(v, OP_Integer, 1, pLevel->iLeftJoin);
+    VdbeComment((v, "record LEFT JOIN hit"));
+    sqlite3ExprCacheClear(pParse);
+    for(pTerm=pWC->a, j=0; j<pWC->nTerm; j++, pTerm++){
+      testcase( pTerm->wtFlags & TERM_VIRTUAL );
+      testcase( pTerm->wtFlags & TERM_CODED );
+      if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;
+      if( (pTerm->prereqAll & pLevel->notReady)!=0 ){
+        assert( pWInfo->untestedTerms );
+        continue;
+      }
+      assert( pTerm->pExpr );
+      sqlite3ExprIfFalse(pParse, pTerm->pExpr, addrCont, SQLITE_JUMPIFNULL);
+      pTerm->wtFlags |= TERM_CODED;
+    }
+  }
+
+  return pLevel->notReady;
+}
+
+#ifdef WHERETRACE_ENABLED
+/*
+** Print the content of a WhereTerm object
+*/
+static void whereTermPrint(WhereTerm *pTerm, int iTerm){
+  if( pTerm==0 ){
+    sqlite3DebugPrintf("TERM-%-3d NULL\n", iTerm);
+  }else{
+    char zType[4];
+    memcpy(zType, "...", 4);
+    if( pTerm->wtFlags & TERM_VIRTUAL ) zType[0] = 'V';
+    if( pTerm->eOperator & WO_EQUIV  ) zType[1] = 'E';
+    if( ExprHasProperty(pTerm->pExpr, EP_FromJoin) ) zType[2] = 'L';
+    sqlite3DebugPrintf("TERM-%-3d %p %s cursor=%-3d prob=%-3d op=0x%03x\n",
+                       iTerm, pTerm, zType, pTerm->leftCursor, pTerm->truthProb,
+                       pTerm->eOperator);
+    sqlite3TreeViewExpr(0, pTerm->pExpr, 0);
+  }
+}
+#endif
+
+#ifdef WHERETRACE_ENABLED
+/*
+** Print a WhereLoop object for debugging purposes
+*/
+static void whereLoopPrint(WhereLoop *p, WhereClause *pWC){
+  WhereInfo *pWInfo = pWC->pWInfo;
+  int nb = 1+(pWInfo->pTabList->nSrc+7)/8;
+  struct SrcList_item *pItem = pWInfo->pTabList->a + p->iTab;
+  Table *pTab = pItem->pTab;
+  sqlite3DebugPrintf("%c%2d.%0*llx.%0*llx", p->cId,
+                     p->iTab, nb, p->maskSelf, nb, p->prereq);
+  sqlite3DebugPrintf(" %12s",
+                     pItem->zAlias ? pItem->zAlias : pTab->zName);
+  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){
+    const char *zName;
+    if( p->u.btree.pIndex && (zName = p->u.btree.pIndex->zName)!=0 ){
+      if( strncmp(zName, "sqlite_autoindex_", 17)==0 ){
+        int i = sqlite3Strlen30(zName) - 1;
+        while( zName[i]!='_' ) i--;
+        zName += i;
+      }
+      sqlite3DebugPrintf(".%-16s %2d", zName, p->u.btree.nEq);
+    }else{
+      sqlite3DebugPrintf("%20s","");
+    }
+  }else{
+    char *z;
+    if( p->u.vtab.idxStr ){
+      z = sqlite3_mprintf("(%d,\"%s\",%x)",
+                p->u.vtab.idxNum, p->u.vtab.idxStr, p->u.vtab.omitMask);
+    }else{
+      z = sqlite3_mprintf("(%d,%x)", p->u.vtab.idxNum, p->u.vtab.omitMask);
+    }
+    sqlite3DebugPrintf(" %-19s", z);
+    sqlite3_free(z);
+  }
+  if( p->wsFlags & WHERE_SKIPSCAN ){
+    sqlite3DebugPrintf(" f %05x %d-%d", p->wsFlags, p->nLTerm,p->u.btree.nSkip);
+  }else{
+    sqlite3DebugPrintf(" f %05x N %d", p->wsFlags, p->nLTerm);
+  }
+  sqlite3DebugPrintf(" cost %d,%d,%d\n", p->rSetup, p->rRun, p->nOut);
+  if( p->nLTerm && (sqlite3WhereTrace & 0x100)!=0 ){
+    int i;
+    for(i=0; i<p->nLTerm; i++){
+      whereTermPrint(p->aLTerm[i], i);
+    }
+  }
+}
+#endif
+
+/*
+** Convert bulk memory into a valid WhereLoop that can be passed
+** to whereLoopClear harmlessly.
+*/
+static void whereLoopInit(WhereLoop *p){
+  p->aLTerm = p->aLTermSpace;
+  p->nLTerm = 0;
+  p->nLSlot = ArraySize(p->aLTermSpace);
+  p->wsFlags = 0;
+}
+
+/*
+** Clear the WhereLoop.u union.  Leave WhereLoop.pLTerm intact.
+*/
+static void whereLoopClearUnion(sqlite3 *db, WhereLoop *p){
+  if( p->wsFlags & (WHERE_VIRTUALTABLE|WHERE_AUTO_INDEX) ){
+    if( (p->wsFlags & WHERE_VIRTUALTABLE)!=0 && p->u.vtab.needFree ){
+      sqlite3_free(p->u.vtab.idxStr);
+      p->u.vtab.needFree = 0;
+      p->u.vtab.idxStr = 0;
+    }else if( (p->wsFlags & WHERE_AUTO_INDEX)!=0 && p->u.btree.pIndex!=0 ){
+      sqlite3DbFree(db, p->u.btree.pIndex->zColAff);
+      sqlite3KeyInfoUnref(p->u.btree.pIndex->pKeyInfo);
+      sqlite3DbFree(db, p->u.btree.pIndex);
+      p->u.btree.pIndex = 0;
+    }
+  }
+}
+
+/*
+** Deallocate internal memory used by a WhereLoop object
+*/
+static void whereLoopClear(sqlite3 *db, WhereLoop *p){
+  if( p->aLTerm!=p->aLTermSpace ) sqlite3DbFree(db, p->aLTerm);
+  whereLoopClearUnion(db, p);
+  whereLoopInit(p);
+}
+
+/*
+** Increase the memory allocation for pLoop->aLTerm[] to be at least n.
+*/
+static int whereLoopResize(sqlite3 *db, WhereLoop *p, int n){
+  WhereTerm **paNew;
+  if( p->nLSlot>=n ) return SQLITE_OK;
+  n = (n+7)&~7;
+  paNew = sqlite3DbMallocRaw(db, sizeof(p->aLTerm[0])*n);
+  if( paNew==0 ) return SQLITE_NOMEM;
+  memcpy(paNew, p->aLTerm, sizeof(p->aLTerm[0])*p->nLSlot);
+  if( p->aLTerm!=p->aLTermSpace ) sqlite3DbFree(db, p->aLTerm);
+  p->aLTerm = paNew;
+  p->nLSlot = n;
+  return SQLITE_OK;
+}
+
+/*
+** Transfer content from the second pLoop into the first.
+*/
+static int whereLoopXfer(sqlite3 *db, WhereLoop *pTo, WhereLoop *pFrom){
+  whereLoopClearUnion(db, pTo);
+  if( whereLoopResize(db, pTo, pFrom->nLTerm) ){
+    memset(&pTo->u, 0, sizeof(pTo->u));
+    return SQLITE_NOMEM;
+  }
+  memcpy(pTo, pFrom, WHERE_LOOP_XFER_SZ);
+  memcpy(pTo->aLTerm, pFrom->aLTerm, pTo->nLTerm*sizeof(pTo->aLTerm[0]));
+  if( pFrom->wsFlags & WHERE_VIRTUALTABLE ){
+    pFrom->u.vtab.needFree = 0;
+  }else if( (pFrom->wsFlags & WHERE_AUTO_INDEX)!=0 ){
+    pFrom->u.btree.pIndex = 0;
+  }
+  return SQLITE_OK;
+}
+
+/*
+** Delete a WhereLoop object
+*/
+static void whereLoopDelete(sqlite3 *db, WhereLoop *p){
+  whereLoopClear(db, p);
+  sqlite3DbFree(db, p);
+}
+
+/*
+** Free a WhereInfo structure
+*/
+static void whereInfoFree(sqlite3 *db, WhereInfo *pWInfo){
+  if( ALWAYS(pWInfo) ){
+    whereClauseClear(&pWInfo->sWC);
+    while( pWInfo->pLoops ){
+      WhereLoop *p = pWInfo->pLoops;
+      pWInfo->pLoops = p->pNextLoop;
+      whereLoopDelete(db, p);
+    }
+    sqlite3DbFree(db, pWInfo);
+  }
+}
+
+/*
+** Return TRUE if both of the following are true:
+**
+**   (1)  X has the same or lower cost that Y
+**   (2)  X is a proper subset of Y
+**
+** By "proper subset" we mean that X uses fewer WHERE clause terms
+** than Y and that every WHERE clause term used by X is also used
+** by Y.
+**
+** If X is a proper subset of Y then Y is a better choice and ought
+** to have a lower cost.  This routine returns TRUE when that cost 
+** relationship is inverted and needs to be adjusted.
+*/
+static int whereLoopCheaperProperSubset(
+  const WhereLoop *pX,       /* First WhereLoop to compare */
+  const WhereLoop *pY        /* Compare against this WhereLoop */
+){
+  int i, j;
+  if( pX->nLTerm >= pY->nLTerm ) return 0; /* X is not a subset of Y */
+  if( pX->rRun >= pY->rRun ){
+    if( pX->rRun > pY->rRun ) return 0;    /* X costs more than Y */
+    if( pX->nOut > pY->nOut ) return 0;    /* X costs more than Y */
+  }
+  for(i=pX->nLTerm-1; i>=0; i--){
+    for(j=pY->nLTerm-1; j>=0; j--){
+      if( pY->aLTerm[j]==pX->aLTerm[i] ) break;
+    }
+    if( j<0 ) return 0;  /* X not a subset of Y since term X[i] not used by Y */
+  }
+  return 1;  /* All conditions meet */
+}
+
+/*
+** Try to adjust the cost of WhereLoop pTemplate upwards or downwards so
+** that:
+**
+**   (1) pTemplate costs less than any other WhereLoops that are a proper
+**       subset of pTemplate
+**
+**   (2) pTemplate costs more than any other WhereLoops for which pTemplate
+**       is a proper subset.
+**
+** To say "WhereLoop X is a proper subset of Y" means that X uses fewer
+** WHERE clause terms than Y and that every WHERE clause term used by X is
+** also used by Y.
+**
+** This adjustment is omitted for SKIPSCAN loops.  In a SKIPSCAN loop, the
+** WhereLoop.nLTerm field is not an accurate measure of the number of WHERE
+** clause terms covered, since some of the first nLTerm entries in aLTerm[]
+** will be NULL (because they are skipped).  That makes it more difficult
+** to compare the loops.  We could add extra code to do the comparison, and
+** perhaps we will someday.  But SKIPSCAN is sufficiently uncommon, and this
+** adjustment is sufficient minor, that it is very difficult to construct
+** a test case where the extra code would improve the query plan.  Better
+** to avoid the added complexity and just omit cost adjustments to SKIPSCAN
+** loops.
+*/
+static void whereLoopAdjustCost(const WhereLoop *p, WhereLoop *pTemplate){
+  if( (pTemplate->wsFlags & WHERE_INDEXED)==0 ) return;
+  if( (pTemplate->wsFlags & WHERE_SKIPSCAN)!=0 ) return;
+  for(; p; p=p->pNextLoop){
+    if( p->iTab!=pTemplate->iTab ) continue;
+    if( (p->wsFlags & WHERE_INDEXED)==0 ) continue;
+    if( (p->wsFlags & WHERE_SKIPSCAN)!=0 ) continue;
+    if( whereLoopCheaperProperSubset(p, pTemplate) ){
+      /* Adjust pTemplate cost downward so that it is cheaper than its 
+      ** subset p */
+      pTemplate->rRun = p->rRun;
+      pTemplate->nOut = p->nOut - 1;
+    }else if( whereLoopCheaperProperSubset(pTemplate, p) ){
+      /* Adjust pTemplate cost upward so that it is costlier than p since
+      ** pTemplate is a proper subset of p */
+      pTemplate->rRun = p->rRun;
+      pTemplate->nOut = p->nOut + 1;
+    }
+  }
+}
+
+/*
+** Search the list of WhereLoops in *ppPrev looking for one that can be
+** supplanted by pTemplate.
+**
+** Return NULL if the WhereLoop list contains an entry that can supplant
+** pTemplate, in other words if pTemplate does not belong on the list.
+**
+** If pX is a WhereLoop that pTemplate can supplant, then return the
+** link that points to pX.
+**
+** If pTemplate cannot supplant any existing element of the list but needs
+** to be added to the list, then return a pointer to the tail of the list.
+*/
+static WhereLoop **whereLoopFindLesser(
+  WhereLoop **ppPrev,
+  const WhereLoop *pTemplate
+){
+  WhereLoop *p;
+  for(p=(*ppPrev); p; ppPrev=&p->pNextLoop, p=*ppPrev){
+    if( p->iTab!=pTemplate->iTab || p->iSortIdx!=pTemplate->iSortIdx ){
+      /* If either the iTab or iSortIdx values for two WhereLoop are different
+      ** then those WhereLoops need to be considered separately.  Neither is
+      ** a candidate to replace the other. */
+      continue;
+    }
+    /* In the current implementation, the rSetup value is either zero
+    ** or the cost of building an automatic index (NlogN) and the NlogN
+    ** is the same for compatible WhereLoops. */
+    assert( p->rSetup==0 || pTemplate->rSetup==0 
+                 || p->rSetup==pTemplate->rSetup );
+
+    /* whereLoopAddBtree() always generates and inserts the automatic index
+    ** case first.  Hence compatible candidate WhereLoops never have a larger
+    ** rSetup. Call this SETUP-INVARIANT */
+    assert( p->rSetup>=pTemplate->rSetup );
+
+    /* Any loop using an appliation-defined index (or PRIMARY KEY or
+    ** UNIQUE constraint) with one or more == constraints is better
+    ** than an automatic index. */
+    if( (p->wsFlags & WHERE_AUTO_INDEX)!=0
+     && (pTemplate->wsFlags & WHERE_INDEXED)!=0
+     && (pTemplate->wsFlags & WHERE_COLUMN_EQ)!=0
+     && (p->prereq & pTemplate->prereq)==pTemplate->prereq
+    ){
+      break;
+    }
+
+    /* If existing WhereLoop p is better than pTemplate, pTemplate can be
+    ** discarded.  WhereLoop p is better if:
+    **   (1)  p has no more dependencies than pTemplate, and
+    **   (2)  p has an equal or lower cost than pTemplate
+    */
+    if( (p->prereq & pTemplate->prereq)==p->prereq    /* (1)  */
+     && p->rSetup<=pTemplate->rSetup                  /* (2a) */
+     && p->rRun<=pTemplate->rRun                      /* (2b) */
+     && p->nOut<=pTemplate->nOut                      /* (2c) */
+    ){
+      return 0;  /* Discard pTemplate */
+    }
+
+    /* If pTemplate is always better than p, then cause p to be overwritten
+    ** with pTemplate.  pTemplate is better than p if:
+    **   (1)  pTemplate has no more dependences than p, and
+    **   (2)  pTemplate has an equal or lower cost than p.
+    */
+    if( (p->prereq & pTemplate->prereq)==pTemplate->prereq   /* (1)  */
+     && p->rRun>=pTemplate->rRun                             /* (2a) */
+     && p->nOut>=pTemplate->nOut                             /* (2b) */
+    ){
+      assert( p->rSetup>=pTemplate->rSetup ); /* SETUP-INVARIANT above */
+      break;   /* Cause p to be overwritten by pTemplate */
+    }
+  }
+  return ppPrev;
+}
+
+/*
+** Insert or replace a WhereLoop entry using the template supplied.
+**
+** An existing WhereLoop entry might be overwritten if the new template
+** is better and has fewer dependencies.  Or the template will be ignored
+** and no insert will occur if an existing WhereLoop is faster and has
+** fewer dependencies than the template.  Otherwise a new WhereLoop is
+** added based on the template.
+**
+** If pBuilder->pOrSet is not NULL then we care about only the
+** prerequisites and rRun and nOut costs of the N best loops.  That
+** information is gathered in the pBuilder->pOrSet object.  This special
+** processing mode is used only for OR clause processing.
+**
+** When accumulating multiple loops (when pBuilder->pOrSet is NULL) we
+** still might overwrite similar loops with the new template if the
+** new template is better.  Loops may be overwritten if the following 
+** conditions are met:
+**
+**    (1)  They have the same iTab.
+**    (2)  They have the same iSortIdx.
+**    (3)  The template has same or fewer dependencies than the current loop
+**    (4)  The template has the same or lower cost than the current loop
+*/
+static int whereLoopInsert(WhereLoopBuilder *pBuilder, WhereLoop *pTemplate){
+  WhereLoop **ppPrev, *p;
+  WhereInfo *pWInfo = pBuilder->pWInfo;
+  sqlite3 *db = pWInfo->pParse->db;
+
+  /* If pBuilder->pOrSet is defined, then only keep track of the costs
+  ** and prereqs.
+  */
+  if( pBuilder->pOrSet!=0 ){
+#if WHERETRACE_ENABLED
+    u16 n = pBuilder->pOrSet->n;
+    int x =
+#endif
+    whereOrInsert(pBuilder->pOrSet, pTemplate->prereq, pTemplate->rRun,
+                                    pTemplate->nOut);
+#if WHERETRACE_ENABLED /* 0x8 */
+    if( sqlite3WhereTrace & 0x8 ){
+      sqlite3DebugPrintf(x?"   or-%d:  ":"   or-X:  ", n);
+      whereLoopPrint(pTemplate, pBuilder->pWC);
+    }
+#endif
+    return SQLITE_OK;
+  }
+
+  /* Look for an existing WhereLoop to replace with pTemplate
+  */
+  whereLoopAdjustCost(pWInfo->pLoops, pTemplate);
+  ppPrev = whereLoopFindLesser(&pWInfo->pLoops, pTemplate);
+
+  if( ppPrev==0 ){
+    /* There already exists a WhereLoop on the list that is better
+    ** than pTemplate, so just ignore pTemplate */
+#if WHERETRACE_ENABLED /* 0x8 */
+    if( sqlite3WhereTrace & 0x8 ){
+      sqlite3DebugPrintf("   skip: ");
+      whereLoopPrint(pTemplate, pBuilder->pWC);
+    }
+#endif
+    return SQLITE_OK;  
+  }else{
+    p = *ppPrev;
+  }
+
+  /* If we reach this point it means that either p[] should be overwritten
+  ** with pTemplate[] if p[] exists, or if p==NULL then allocate a new
+  ** WhereLoop and insert it.
+  */
+#if WHERETRACE_ENABLED /* 0x8 */
+  if( sqlite3WhereTrace & 0x8 ){
+    if( p!=0 ){
+      sqlite3DebugPrintf("replace: ");
+      whereLoopPrint(p, pBuilder->pWC);
+    }
+    sqlite3DebugPrintf("    add: ");
+    whereLoopPrint(pTemplate, pBuilder->pWC);
+  }
+#endif
+  if( p==0 ){
+    /* Allocate a new WhereLoop to add to the end of the list */
+    *ppPrev = p = sqlite3DbMallocRaw(db, sizeof(WhereLoop));
+    if( p==0 ) return SQLITE_NOMEM;
+    whereLoopInit(p);
+    p->pNextLoop = 0;
+  }else{
+    /* We will be overwriting WhereLoop p[].  But before we do, first
+    ** go through the rest of the list and delete any other entries besides
+    ** p[] that are also supplated by pTemplate */
+    WhereLoop **ppTail = &p->pNextLoop;
+    WhereLoop *pToDel;
+    while( *ppTail ){
+      ppTail = whereLoopFindLesser(ppTail, pTemplate);
+      if( ppTail==0 ) break;
+      pToDel = *ppTail;
+      if( pToDel==0 ) break;
+      *ppTail = pToDel->pNextLoop;
+#if WHERETRACE_ENABLED /* 0x8 */
+      if( sqlite3WhereTrace & 0x8 ){
+        sqlite3DebugPrintf(" delete: ");
+        whereLoopPrint(pToDel, pBuilder->pWC);
+      }
+#endif
+      whereLoopDelete(db, pToDel);
+    }
+  }
+  whereLoopXfer(db, p, pTemplate);
+  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){
+    Index *pIndex = p->u.btree.pIndex;
+    if( pIndex && pIndex->tnum==0 ){
+      p->u.btree.pIndex = 0;
+    }
+  }
+  return SQLITE_OK;
+}
+
+/*
+** Adjust the WhereLoop.nOut value downward to account for terms of the
+** WHERE clause that reference the loop but which are not used by an
+** index.
+**
+** In the current implementation, the first extra WHERE clause term reduces
+** the number of output rows by a factor of 10 and each additional term
+** reduces the number of output rows by sqrt(2).
+*/
+static void whereLoopOutputAdjust(
+  WhereClause *pWC,      /* The WHERE clause */
+  WhereLoop *pLoop,      /* The loop to adjust downward */
+  LogEst nRow            /* Number of rows in the entire table */
+){
+  WhereTerm *pTerm, *pX;
+  Bitmask notAllowed = ~(pLoop->prereq|pLoop->maskSelf);
+  int i, j;
+  int nEq = 0;    /* Number of = constraints not within likely()/unlikely() */
+
+  for(i=pWC->nTerm, pTerm=pWC->a; i>0; i--, pTerm++){
+    if( (pTerm->wtFlags & TERM_VIRTUAL)!=0 ) break;
+    if( (pTerm->prereqAll & pLoop->maskSelf)==0 ) continue;
+    if( (pTerm->prereqAll & notAllowed)!=0 ) continue;
+    for(j=pLoop->nLTerm-1; j>=0; j--){
+      pX = pLoop->aLTerm[j];
+      if( pX==0 ) continue;
+      if( pX==pTerm ) break;
+      if( pX->iParent>=0 && (&pWC->a[pX->iParent])==pTerm ) break;
+    }
+    if( j<0 ){
+      if( pTerm->truthProb<=0 ){
+        pLoop->nOut += pTerm->truthProb;
+      }else{
+        pLoop->nOut--;
+        if( pTerm->eOperator&WO_EQ ) nEq++;
+      }
+    }
+  }
+  /* TUNING:  If there is at least one equality constraint in the WHERE
+  ** clause that does not have a likelihood() explicitly assigned to it
+  ** then do not let the estimated number of output rows exceed half 
+  ** the number of rows in the table. */
+  if( nEq && pLoop->nOut>nRow-10 ){
+    pLoop->nOut = nRow - 10;
+  }
+}
+
+/*
+** Adjust the cost C by the costMult facter T.  This only occurs if
+** compiled with -DSQLITE_ENABLE_COSTMULT
+*/
+#ifdef SQLITE_ENABLE_COSTMULT
+# define ApplyCostMultiplier(C,T)  C += T
+#else
+# define ApplyCostMultiplier(C,T)
+#endif
+
+/*
+** We have so far matched pBuilder->pNew->u.btree.nEq terms of the 
+** index pIndex. Try to match one more.
+**
+** When this function is called, pBuilder->pNew->nOut contains the 
+** number of rows expected to be visited by filtering using the nEq 
+** terms only. If it is modified, this value is restored before this 
+** function returns.
+**
+** If pProbe->tnum==0, that means pIndex is a fake index used for the
+** INTEGER PRIMARY KEY.
+*/
+static int whereLoopAddBtreeIndex(
+  WhereLoopBuilder *pBuilder,     /* The WhereLoop factory */
+  struct SrcList_item *pSrc,      /* FROM clause term being analyzed */
+  Index *pProbe,                  /* An index on pSrc */
+  LogEst nInMul                   /* log(Number of iterations due to IN) */
+){
+  WhereInfo *pWInfo = pBuilder->pWInfo;  /* WHERE analyse context */
+  Parse *pParse = pWInfo->pParse;        /* Parsing context */
+  sqlite3 *db = pParse->db;       /* Database connection malloc context */
+  WhereLoop *pNew;                /* Template WhereLoop under construction */
+  WhereTerm *pTerm;               /* A WhereTerm under consideration */
+  int opMask;                     /* Valid operators for constraints */
+  WhereScan scan;                 /* Iterator for WHERE terms */
+  Bitmask saved_prereq;           /* Original value of pNew->prereq */
+  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
+  u16 saved_nEq;                  /* Original value of pNew->u.btree.nEq */
+  u16 saved_nSkip;                /* Original value of pNew->u.btree.nSkip */
+  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */
+  LogEst saved_nOut;              /* Original value of pNew->nOut */
+  int iCol;                       /* Index of the column in the table */
+  int rc = SQLITE_OK;             /* Return code */
+  LogEst rSize;                   /* Number of rows in the table */
+  LogEst rLogSize;                /* Logarithm of table size */
+  WhereTerm *pTop = 0, *pBtm = 0; /* Top and bottom range constraints */
+
+  pNew = pBuilder->pNew;
+  if( db->mallocFailed ) return SQLITE_NOMEM;
+
+  assert( (pNew->wsFlags & WHERE_VIRTUALTABLE)==0 );
+  assert( (pNew->wsFlags & WHERE_TOP_LIMIT)==0 );
+  if( pNew->wsFlags & WHERE_BTM_LIMIT ){
+    opMask = WO_LT|WO_LE;
+  }else if( pProbe->tnum<=0 || (pSrc->jointype & JT_LEFT)!=0 ){
+    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE;
+  }else{
+    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
+  }
+  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);
+
+  assert( pNew->u.btree.nEq<pProbe->nColumn );
+  iCol = pProbe->aiColumn[pNew->u.btree.nEq];
+
+  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
+                        opMask, pProbe);
+  saved_nEq = pNew->u.btree.nEq;
+  saved_nSkip = pNew->u.btree.nSkip;
+  saved_nLTerm = pNew->nLTerm;
+  saved_wsFlags = pNew->wsFlags;
+  saved_prereq = pNew->prereq;
+  saved_nOut = pNew->nOut;
+  pNew->rSetup = 0;
+  rSize = pProbe->aiRowLogEst[0];
+  rLogSize = estLog(rSize);
+
+  /* Consider using a skip-scan if there are no WHERE clause constraints
+  ** available for the left-most terms of the index, and if the average
+  ** number of repeats in the left-most terms is at least 18. 
+  **
+  ** The magic number 18 is selected on the basis that scanning 17 rows
+  ** is almost always quicker than an index seek (even though if the index
+  ** contains fewer than 2^17 rows we assume otherwise in other parts of
+  ** the code). And, even if it is not, it should not be too much slower. 
+  ** On the other hand, the extra seeks could end up being significantly
+  ** more expensive.  */
+  assert( 42==sqlite3LogEst(18) );
+  if( saved_nEq==saved_nSkip
+   && saved_nEq+1<pProbe->nKeyCol
+   && pProbe->aiRowLogEst[saved_nEq+1]>=42  /* TUNING: Minimum for skip-scan */
+   && (rc = whereLoopResize(db, pNew, pNew->nLTerm+1))==SQLITE_OK
+  ){
+    LogEst nIter;
+    pNew->u.btree.nEq++;
+    pNew->u.btree.nSkip++;
+    pNew->aLTerm[pNew->nLTerm++] = 0;
+    pNew->wsFlags |= WHERE_SKIPSCAN;
+    nIter = pProbe->aiRowLogEst[saved_nEq] - pProbe->aiRowLogEst[saved_nEq+1];
+    if( pTerm ){
+      /* TUNING:  When estimating skip-scan for a term that is also indexable,
+      ** multiply the cost of the skip-scan by 2.0, to make it a little less
+      ** desirable than the regular index lookup. */
+      nIter += 10;  assert( 10==sqlite3LogEst(2) );
+    }
+    pNew->nOut -= nIter;
+    /* TUNING:  Because uncertainties in the estimates for skip-scan queries,
+    ** add a 1.375 fudge factor to make skip-scan slightly less likely. */
+    nIter += 5;
+    whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nIter + nInMul);
+    pNew->nOut = saved_nOut;
+    pNew->u.btree.nEq = saved_nEq;
+    pNew->u.btree.nSkip = saved_nSkip;
+  }
+  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
+    u16 eOp = pTerm->eOperator;   /* Shorthand for pTerm->eOperator */
+    LogEst rCostIdx;
+    LogEst nOutUnadjusted;        /* nOut before IN() and WHERE adjustments */
+    int nIn = 0;
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+    int nRecValid = pBuilder->nRecValid;
+#endif
+    if( (eOp==WO_ISNULL || (pTerm->wtFlags&TERM_VNULL)!=0)
+     && (iCol<0 || pSrc->pTab->aCol[iCol].notNull)
+    ){
+      continue; /* ignore IS [NOT] NULL constraints on NOT NULL columns */
+    }
+    if( pTerm->prereqRight & pNew->maskSelf ) continue;
+
+    pNew->wsFlags = saved_wsFlags;
+    pNew->u.btree.nEq = saved_nEq;
+    pNew->nLTerm = saved_nLTerm;
+    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
+    pNew->aLTerm[pNew->nLTerm++] = pTerm;
+    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
+
+    assert( nInMul==0
+        || (pNew->wsFlags & WHERE_COLUMN_NULL)!=0 
+        || (pNew->wsFlags & WHERE_COLUMN_IN)!=0 
+        || (pNew->wsFlags & WHERE_SKIPSCAN)!=0 
+    );
+
+    if( eOp & WO_IN ){
+      Expr *pExpr = pTerm->pExpr;
+      pNew->wsFlags |= WHERE_COLUMN_IN;
+      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
+        /* "x IN (SELECT ...)":  TUNING: the SELECT returns 25 rows */
+        nIn = 46;  assert( 46==sqlite3LogEst(25) );
+      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
+        /* "x IN (value, value, ...)" */
+        nIn = sqlite3LogEst(pExpr->x.pList->nExpr);
+      }
+      assert( nIn>0 );  /* RHS always has 2 or more terms...  The parser
+                        ** changes "x IN (?)" into "x=?". */
+
+    }else if( eOp & (WO_EQ) ){
+      pNew->wsFlags |= WHERE_COLUMN_EQ;
+      if( iCol<0 || (nInMul==0 && pNew->u.btree.nEq==pProbe->nKeyCol-1) ){
+        if( iCol>=0 && !IsUniqueIndex(pProbe) ){
+          pNew->wsFlags |= WHERE_UNQ_WANTED;
+        }else{
+          pNew->wsFlags |= WHERE_ONEROW;
+        }
+      }
+    }else if( eOp & WO_ISNULL ){
+      pNew->wsFlags |= WHERE_COLUMN_NULL;
+    }else if( eOp & (WO_GT|WO_GE) ){
+      testcase( eOp & WO_GT );
+      testcase( eOp & WO_GE );
+      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
+      pBtm = pTerm;
+      pTop = 0;
+    }else{
+      assert( eOp & (WO_LT|WO_LE) );
+      testcase( eOp & WO_LT );
+      testcase( eOp & WO_LE );
+      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
+      pTop = pTerm;
+      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
+                     pNew->aLTerm[pNew->nLTerm-2] : 0;
+    }
+
+    /* At this point pNew->nOut is set to the number of rows expected to
+    ** be visited by the index scan before considering term pTerm, or the
+    ** values of nIn and nInMul. In other words, assuming that all 
+    ** "x IN(...)" terms are replaced with "x = ?". This block updates
+    ** the value of pNew->nOut to account for pTerm (but not nIn/nInMul).  */
+    assert( pNew->nOut==saved_nOut );
+    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
+      /* Adjust nOut using stat3/stat4 data. Or, if there is no stat3/stat4
+      ** data, using some other estimate.  */
+      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, pNew);
+    }else{
+      int nEq = ++pNew->u.btree.nEq;
+      assert( eOp & (WO_ISNULL|WO_EQ|WO_IN) );
+
+      assert( pNew->nOut==saved_nOut );
+      if( pTerm->truthProb<=0 && iCol>=0 ){
+        assert( (eOp & WO_IN) || nIn==0 );
+        testcase( eOp & WO_IN );
+        pNew->nOut += pTerm->truthProb;
+        pNew->nOut -= nIn;
+      }else{
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+        tRowcnt nOut = 0;
+        if( nInMul==0 
+         && pProbe->nSample 
+         && pNew->u.btree.nEq<=pProbe->nSampleCol
+         && OptimizationEnabled(db, SQLITE_Stat3) 
+         && ((eOp & WO_IN)==0 || !ExprHasProperty(pTerm->pExpr, EP_xIsSelect))
+        ){
+          Expr *pExpr = pTerm->pExpr;
+          if( (eOp & (WO_EQ|WO_ISNULL))!=0 ){
+            testcase( eOp & WO_EQ );
+            testcase( eOp & WO_ISNULL );
+            rc = whereEqualScanEst(pParse, pBuilder, pExpr->pRight, &nOut);
+          }else{
+            rc = whereInScanEst(pParse, pBuilder, pExpr->x.pList, &nOut);
+          }
+          if( rc==SQLITE_NOTFOUND ) rc = SQLITE_OK;
+          if( rc!=SQLITE_OK ) break;          /* Jump out of the pTerm loop */
+          if( nOut ){
+            pNew->nOut = sqlite3LogEst(nOut);
+            if( pNew->nOut>saved_nOut ) pNew->nOut = saved_nOut;
+            pNew->nOut -= nIn;
+          }
+        }
+        if( nOut==0 )
+#endif
+        {
+          pNew->nOut += (pProbe->aiRowLogEst[nEq] - pProbe->aiRowLogEst[nEq-1]);
+          if( eOp & WO_ISNULL ){
+            /* TUNING: If there is no likelihood() value, assume that a 
+            ** "col IS NULL" expression matches twice as many rows 
+            ** as (col=?). */
+            pNew->nOut += 10;
+          }
+        }
+      }
+    }
+
+    /* Set rCostIdx to the cost of visiting selected rows in index. Add
+    ** it to pNew->rRun, which is currently set to the cost of the index
+    ** seek only. Then, if this is a non-covering index, add the cost of
+    ** visiting the rows in the main table.  */
+    rCostIdx = pNew->nOut + 1 + (15*pProbe->szIdxRow)/pSrc->pTab->szTabRow;
+    pNew->rRun = sqlite3LogEstAdd(rLogSize, rCostIdx);
+    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
+      pNew->rRun = sqlite3LogEstAdd(pNew->rRun, pNew->nOut + 16);
+    }
+    ApplyCostMultiplier(pNew->rRun, pProbe->pTable->costMult);
+
+    nOutUnadjusted = pNew->nOut;
+    pNew->rRun += nInMul + nIn;
+    pNew->nOut += nInMul + nIn;
+    whereLoopOutputAdjust(pBuilder->pWC, pNew, rSize);
+    rc = whereLoopInsert(pBuilder, pNew);
+
+    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
+      pNew->nOut = saved_nOut;
+    }else{
+      pNew->nOut = nOutUnadjusted;
+    }
+
+    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
+     && pNew->u.btree.nEq<pProbe->nColumn
+    ){
+      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
+    }
+    pNew->nOut = saved_nOut;
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+    pBuilder->nRecValid = nRecValid;
+#endif
+  }
+  pNew->prereq = saved_prereq;
+  pNew->u.btree.nEq = saved_nEq;
+  pNew->u.btree.nSkip = saved_nSkip;
+  pNew->wsFlags = saved_wsFlags;
+  pNew->nOut = saved_nOut;
+  pNew->nLTerm = saved_nLTerm;
+  return rc;
+}
+
+/*
+** Return True if it is possible that pIndex might be useful in
+** implementing the ORDER BY clause in pBuilder.
+**
+** Return False if pBuilder does not contain an ORDER BY clause or
+** if there is no way for pIndex to be useful in implementing that
+** ORDER BY clause.
+*/
+static int indexMightHelpWithOrderBy(
+  WhereLoopBuilder *pBuilder,
+  Index *pIndex,
+  int iCursor
+){
+  ExprList *pOB;
+  int ii, jj;
+
+  if( pIndex->bUnordered ) return 0;
+  if( (pOB = pBuilder->pWInfo->pOrderBy)==0 ) return 0;
+  for(ii=0; ii<pOB->nExpr; ii++){
+    Expr *pExpr = sqlite3ExprSkipCollate(pOB->a[ii].pExpr);
+    if( pExpr->op!=TK_COLUMN ) return 0;
+    if( pExpr->iTable==iCursor ){
+      if( pExpr->iColumn<0 ) return 1;
+      for(jj=0; jj<pIndex->nKeyCol; jj++){
+        if( pExpr->iColumn==pIndex->aiColumn[jj] ) return 1;
+      }
+    }
+  }
+  return 0;
+}
+
+/*
+** Return a bitmask where 1s indicate that the corresponding column of
+** the table is used by an index.  Only the first 63 columns are considered.
+*/
+static Bitmask columnsInIndex(Index *pIdx){
+  Bitmask m = 0;
+  int j;
+  for(j=pIdx->nColumn-1; j>=0; j--){
+    int x = pIdx->aiColumn[j];
+    if( x>=0 ){
+      testcase( x==BMS-1 );
+      testcase( x==BMS-2 );
+      if( x<BMS-1 ) m |= MASKBIT(x);
+    }
+  }
+  return m;
+}
+
+/* Check to see if a partial index with pPartIndexWhere can be used
+** in the current query.  Return true if it can be and false if not.
+*/
+static int whereUsablePartialIndex(int iTab, WhereClause *pWC, Expr *pWhere){
+  int i;
+  WhereTerm *pTerm;
+  for(i=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
+    if( sqlite3ExprImpliesExpr(pTerm->pExpr, pWhere, iTab) ) return 1;
+  }
+  return 0;
+}
+
+/*
+** Add all WhereLoop objects for a single table of the join where the table
+** is idenfied by pBuilder->pNew->iTab.  That table is guaranteed to be
+** a b-tree table, not a virtual table.
+**
+** The costs (WhereLoop.rRun) of the b-tree loops added by this function
+** are calculated as follows:
+**
+** For a full scan, assuming the table (or index) contains nRow rows:
+**
+**     cost = nRow * 3.0                    // full-table scan
+**     cost = nRow * K                      // scan of covering index
+**     cost = nRow * (K+3.0)                // scan of non-covering index
+**
+** where K is a value between 1.1 and 3.0 set based on the relative 
+** estimated average size of the index and table records.
+**
+** For an index scan, where nVisit is the number of index rows visited
+** by the scan, and nSeek is the number of seek operations required on 
+** the index b-tree:
+**
+**     cost = nSeek * (log(nRow) + K * nVisit)          // covering index
+**     cost = nSeek * (log(nRow) + (K+3.0) * nVisit)    // non-covering index
+**
+** Normally, nSeek is 1. nSeek values greater than 1 come about if the 
+** WHERE clause includes "x IN (....)" terms used in place of "x=?". Or when 
+** implicit "x IN (SELECT x FROM tbl)" terms are added for skip-scans.
+**
+** The estimated values (nRow, nVisit, nSeek) often contain a large amount
+** of uncertainty.  For this reason, scoring is designed to pick plans that
+** "do the least harm" if the estimates are inaccurate.  For example, a
+** log(nRow) factor is omitted from a non-covering index scan in order to
+** bias the scoring in favor of using an index, since the worst-case
+** performance of using an index is far better than the worst-case performance
+** of a full table scan.
+*/
+static int whereLoopAddBtree(
+  WhereLoopBuilder *pBuilder, /* WHERE clause information */
+  Bitmask mExtra              /* Extra prerequesites for using this table */
+){
+  WhereInfo *pWInfo;          /* WHERE analysis context */
+  Index *pProbe;              /* An index we are evaluating */
+  Index sPk;                  /* A fake index object for the primary key */
+  LogEst aiRowEstPk[2];       /* The aiRowLogEst[] value for the sPk index */
+  i16 aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
+  SrcList *pTabList;          /* The FROM clause */
+  struct SrcList_item *pSrc;  /* The FROM clause btree term to add */
+  WhereLoop *pNew;            /* Template WhereLoop object */
+  int rc = SQLITE_OK;         /* Return code */
+  int iSortIdx = 1;           /* Index number */
+  int b;                      /* A boolean value */
+  LogEst rSize;               /* number of rows in the table */
+  LogEst rLogSize;            /* Logarithm of the number of rows in the table */
+  WhereClause *pWC;           /* The parsed WHERE clause */
+  Table *pTab;                /* Table being queried */
+  
+  pNew = pBuilder->pNew;
+  pWInfo = pBuilder->pWInfo;
+  pTabList = pWInfo->pTabList;
+  pSrc = pTabList->a + pNew->iTab;
+  pTab = pSrc->pTab;
+  pWC = pBuilder->pWC;
+  assert( !IsVirtual(pSrc->pTab) );
+
+  if( pSrc->pIndex ){
+    /* An INDEXED BY clause specifies a particular index to use */
+    pProbe = pSrc->pIndex;
+  }else if( !HasRowid(pTab) ){
+    pProbe = pTab->pIndex;
+  }else{
+    /* There is no INDEXED BY clause.  Create a fake Index object in local
+    ** variable sPk to represent the rowid primary key index.  Make this
+    ** fake index the first in a chain of Index objects with all of the real
+    ** indices to follow */
+    Index *pFirst;                  /* First of real indices on the table */
+    memset(&sPk, 0, sizeof(Index));
+    sPk.nKeyCol = 1;
+    sPk.nColumn = 1;
+    sPk.aiColumn = &aiColumnPk;
+    sPk.aiRowLogEst = aiRowEstPk;
+    sPk.onError = OE_Replace;
+    sPk.pTable = pTab;
+    sPk.szIdxRow = pTab->szTabRow;
+    aiRowEstPk[0] = pTab->nRowLogEst;
+    aiRowEstPk[1] = 0;
+    pFirst = pSrc->pTab->pIndex;
+    if( pSrc->notIndexed==0 ){
+      /* The real indices of the table are only considered if the
+      ** NOT INDEXED qualifier is omitted from the FROM clause */
+      sPk.pNext = pFirst;
+    }
+    pProbe = &sPk;
+  }
+  rSize = pTab->nRowLogEst;
+  rLogSize = estLog(rSize);
+
+#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
+  /* Automatic indexes */
+  if( !pBuilder->pOrSet
+   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0
+   && pSrc->pIndex==0
+   && !pSrc->viaCoroutine
+   && !pSrc->notIndexed
+   && HasRowid(pTab)
+   && !pSrc->isCorrelated
+   && !pSrc->isRecursive
+  ){
+    /* Generate auto-index WhereLoops */
+    WhereTerm *pTerm;
+    WhereTerm *pWCEnd = pWC->a + pWC->nTerm;
+    for(pTerm=pWC->a; rc==SQLITE_OK && pTerm<pWCEnd; pTerm++){
+      if( pTerm->prereqRight & pNew->maskSelf ) continue;
+      if( termCanDriveIndex(pTerm, pSrc, 0) ){
+        pNew->u.btree.nEq = 1;
+        pNew->u.btree.nSkip = 0;
+        pNew->u.btree.pIndex = 0;
+        pNew->nLTerm = 1;
+        pNew->aLTerm[0] = pTerm;
+        /* TUNING: One-time cost for computing the automatic index is
+        ** estimated to be X*N*log2(N) where N is the number of rows in
+        ** the table being indexed and where X is 7 (LogEst=28) for normal
+        ** tables or 1.375 (LogEst=4) for views and subqueries.  The value
+        ** of X is smaller for views and subqueries so that the query planner
+        ** will be more aggressive about generating automatic indexes for
+        ** those objects, since there is no opportunity to add schema
+        ** indexes on subqueries and views. */
+        pNew->rSetup = rLogSize + rSize + 4;
+        if( pTab->pSelect==0 && (pTab->tabFlags & TF_Ephemeral)==0 ){
+          pNew->rSetup += 24;
+        }
+        ApplyCostMultiplier(pNew->rSetup, pTab->costMult);
+        /* TUNING: Each index lookup yields 20 rows in the table.  This
+        ** is more than the usual guess of 10 rows, since we have no way
+        ** of knowing how selective the index will ultimately be.  It would
+        ** not be unreasonable to make this value much larger. */
+        pNew->nOut = 43;  assert( 43==sqlite3LogEst(20) );
+        pNew->rRun = sqlite3LogEstAdd(rLogSize,pNew->nOut);
+        pNew->wsFlags = WHERE_AUTO_INDEX;
+        pNew->prereq = mExtra | pTerm->prereqRight;
+        rc = whereLoopInsert(pBuilder, pNew);
+      }
+    }
+  }
+#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */
+
+  /* Loop over all indices
+  */
+  for(; rc==SQLITE_OK && pProbe; pProbe=pProbe->pNext, iSortIdx++){
+    if( pProbe->pPartIdxWhere!=0
+     && !whereUsablePartialIndex(pSrc->iCursor, pWC, pProbe->pPartIdxWhere) ){
+      testcase( pNew->iTab!=pSrc->iCursor );  /* See ticket [98d973b8f5] */
+      continue;  /* Partial index inappropriate for this query */
+    }
+    rSize = pProbe->aiRowLogEst[0];
+    pNew->u.btree.nEq = 0;
+    pNew->u.btree.nSkip = 0;
+    pNew->nLTerm = 0;
+    pNew->iSortIdx = 0;
+    pNew->rSetup = 0;
+    pNew->prereq = mExtra;
+    pNew->nOut = rSize;
+    pNew->u.btree.pIndex = pProbe;
+    b = indexMightHelpWithOrderBy(pBuilder, pProbe, pSrc->iCursor);
+    /* The ONEPASS_DESIRED flags never occurs together with ORDER BY */
+    assert( (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || b==0 );
+    if( pProbe->tnum<=0 ){
+      /* Integer primary key index */
+      pNew->wsFlags = WHERE_IPK;
+
+      /* Full table scan */
+      pNew->iSortIdx = b ? iSortIdx : 0;
+      /* TUNING: Cost of full table scan is (N*3.0). */
+      pNew->rRun = rSize + 16;
+      ApplyCostMultiplier(pNew->rRun, pTab->costMult);
+      whereLoopOutputAdjust(pWC, pNew, rSize);
+      rc = whereLoopInsert(pBuilder, pNew);
+      pNew->nOut = rSize;
+      if( rc ) break;
+    }else{
+      Bitmask m;
+      if( pProbe->isCovering ){
+        pNew->wsFlags = WHERE_IDX_ONLY | WHERE_INDEXED;
+        m = 0;
+      }else{
+        m = pSrc->colUsed & ~columnsInIndex(pProbe);
+        pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;
+      }
+
+      /* Full scan via index */
+      if( b
+       || !HasRowid(pTab)
+       || ( m==0
+         && pProbe->bUnordered==0
+         && (pProbe->szIdxRow<pTab->szTabRow)
+         && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
+         && sqlite3GlobalConfig.bUseCis
+         && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
+          )
+      ){
+        pNew->iSortIdx = b ? iSortIdx : 0;
+
+        /* The cost of visiting the index rows is N*K, where K is
+        ** between 1.1 and 3.0, depending on the relative sizes of the
+        ** index and table rows. If this is a non-covering index scan,
+        ** also add the cost of visiting table rows (N*3.0).  */
+        pNew->rRun = rSize + 1 + (15*pProbe->szIdxRow)/pTab->szTabRow;
+        if( m!=0 ){
+          pNew->rRun = sqlite3LogEstAdd(pNew->rRun, rSize+16);
+        }
+        ApplyCostMultiplier(pNew->rRun, pTab->costMult);
+        whereLoopOutputAdjust(pWC, pNew, rSize);
+        rc = whereLoopInsert(pBuilder, pNew);
+        pNew->nOut = rSize;
+        if( rc ) break;
+      }
+    }
+
+    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);
+#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
+    sqlite3Stat4ProbeFree(pBuilder->pRec);
+    pBuilder->nRecValid = 0;
+    pBuilder->pRec = 0;
+#endif
+
+    /* If there was an INDEXED BY clause, then only that one index is
+    ** considered. */
+    if( pSrc->pIndex ) break;
+  }
+  return rc;
+}
+
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+/*
+** Add all WhereLoop objects for a table of the join identified by
+** pBuilder->pNew->iTab.  That table is guaranteed to be a virtual table.
+*/
+static int whereLoopAddVirtual(
+  WhereLoopBuilder *pBuilder,  /* WHERE clause information */
+  Bitmask mExtra
+){
+  WhereInfo *pWInfo;           /* WHERE analysis context */
+  Parse *pParse;               /* The parsing context */
+  WhereClause *pWC;            /* The WHERE clause */
+  struct SrcList_item *pSrc;   /* The FROM clause term to search */
+  Table *pTab;
+  sqlite3 *db;
+  sqlite3_index_info *pIdxInfo;
+  struct sqlite3_index_constraint *pIdxCons;
+  struct sqlite3_index_constraint_usage *pUsage;
+  WhereTerm *pTerm;
+  int i, j;
+  int iTerm, mxTerm;
+  int nConstraint;
+  int seenIn = 0;              /* True if an IN operator is seen */
+  int seenVar = 0;             /* True if a non-constant constraint is seen */
+  int iPhase;                  /* 0: const w/o IN, 1: const, 2: no IN,  2: IN */
+  WhereLoop *pNew;
+  int rc = SQLITE_OK;
+
+  pWInfo = pBuilder->pWInfo;
+  pParse = pWInfo->pParse;
+  db = pParse->db;
+  pWC = pBuilder->pWC;
+  pNew = pBuilder->pNew;
+  pSrc = &pWInfo->pTabList->a[pNew->iTab];
+  pTab = pSrc->pTab;
+  assert( IsVirtual(pTab) );
+  pIdxInfo = allocateIndexInfo(pParse, pWC, pSrc, pBuilder->pOrderBy);
+  if( pIdxInfo==0 ) return SQLITE_NOMEM;
+  pNew->prereq = 0;
+  pNew->rSetup = 0;
+  pNew->wsFlags = WHERE_VIRTUALTABLE;
+  pNew->nLTerm = 0;
+  pNew->u.vtab.needFree = 0;
+  pUsage = pIdxInfo->aConstraintUsage;
+  nConstraint = pIdxInfo->nConstraint;
+  if( whereLoopResize(db, pNew, nConstraint) ){
+    sqlite3DbFree(db, pIdxInfo);
+    return SQLITE_NOMEM;
+  }
+
+  for(iPhase=0; iPhase<=3; iPhase++){
+    if( !seenIn && (iPhase&1)!=0 ){
+      iPhase++;
+      if( iPhase>3 ) break;
+    }
+    if( !seenVar && iPhase>1 ) break;
+    pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
+    for(i=0; i<pIdxInfo->nConstraint; i++, pIdxCons++){
+      j = pIdxCons->iTermOffset;
+      pTerm = &pWC->a[j];
+      switch( iPhase ){
+        case 0:    /* Constants without IN operator */
+          pIdxCons->usable = 0;
+          if( (pTerm->eOperator & WO_IN)!=0 ){
+            seenIn = 1;
+          }
+          if( pTerm->prereqRight!=0 ){
+            seenVar = 1;
+          }else if( (pTerm->eOperator & WO_IN)==0 ){
+            pIdxCons->usable = 1;
+          }
+          break;
+        case 1:    /* Constants with IN operators */
+          assert( seenIn );
+          pIdxCons->usable = (pTerm->prereqRight==0);
+          break;
+        case 2:    /* Variables without IN */
+          assert( seenVar );
+          pIdxCons->usable = (pTerm->eOperator & WO_IN)==0;
+          break;
+        default:   /* Variables with IN */
+          assert( seenVar && seenIn );
+          pIdxCons->usable = 1;
+          break;
+      }
+    }
+    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 / (double)2;
+    pIdxInfo->estimatedRows = 25;
+    rc = vtabBestIndex(pParse, pTab, pIdxInfo);
+    if( rc ) goto whereLoopAddVtab_exit;
+    pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
+    pNew->prereq = mExtra;
+    mxTerm = -1;
+    assert( pNew->nLSlot>=nConstraint );
+    for(i=0; i<nConstraint; i++) pNew->aLTerm[i] = 0;
+    pNew->u.vtab.omitMask = 0;
+    for(i=0; i<nConstraint; i++, pIdxCons++){
+      if( (iTerm = pUsage[i].argvIndex - 1)>=0 ){
+        j = pIdxCons->iTermOffset;
+        if( iTerm>=nConstraint
+         || j<0
+         || j>=pWC->nTerm
+         || pNew->aLTerm[iTerm]!=0
+        ){
+          rc = SQLITE_ERROR;
+          sqlite3ErrorMsg(pParse, "%s.xBestIndex() malfunction", pTab->zName);
+          goto whereLoopAddVtab_exit;
+        }
+        testcase( iTerm==nConstraint-1 );
+        testcase( j==0 );
+        testcase( j==pWC->nTerm-1 );
+        pTerm = &pWC->a[j];
+        pNew->prereq |= pTerm->prereqRight;
+        assert( iTerm<pNew->nLSlot );
+        pNew->aLTerm[iTerm] = pTerm;
+        if( iTerm>mxTerm ) mxTerm = iTerm;
+        testcase( iTerm==15 );
+        testcase( iTerm==16 );
+        if( iTerm<16 && pUsage[i].omit ) pNew->u.vtab.omitMask |= 1<<iTerm;
+        if( (pTerm->eOperator & WO_IN)!=0 ){
+          if( pUsage[i].omit==0 ){
+            /* Do not attempt to use an IN constraint if the virtual table
+            ** says that the equivalent EQ constraint cannot be safely omitted.
+            ** If we do attempt to use such a constraint, some rows might be
+            ** repeated in the output. */
+            break;
+          }
+          /* A virtual table that is constrained by an IN clause may not
+          ** consume the ORDER BY clause because (1) the order of IN terms
+          ** is not necessarily related to the order of output terms and
+          ** (2) Multiple outputs from a single IN value will not merge
+          ** together.  */
+          pIdxInfo->orderByConsumed = 0;
+        }
+      }
+    }
+    if( i>=nConstraint ){
+      pNew->nLTerm = mxTerm+1;
+      assert( pNew->nLTerm<=pNew->nLSlot );
+      pNew->u.vtab.idxNum = pIdxInfo->idxNum;
+      pNew->u.vtab.needFree = pIdxInfo->needToFreeIdxStr;
+      pIdxInfo->needToFreeIdxStr = 0;
+      pNew->u.vtab.idxStr = pIdxInfo->idxStr;
+      pNew->u.vtab.isOrdered = (i8)(pIdxInfo->orderByConsumed ?
+                                      pIdxInfo->nOrderBy : 0);
+      pNew->rSetup = 0;
+      pNew->rRun = sqlite3LogEstFromDouble(pIdxInfo->estimatedCost);
+      pNew->nOut = sqlite3LogEst(pIdxInfo->estimatedRows);
+      whereLoopInsert(pBuilder, pNew);
+      if( pNew->u.vtab.needFree ){
+        sqlite3_free(pNew->u.vtab.idxStr);
+        pNew->u.vtab.needFree = 0;
+      }
+    }
+  }  
+
+whereLoopAddVtab_exit:
+  if( pIdxInfo->needToFreeIdxStr ) sqlite3_free(pIdxInfo->idxStr);
+  sqlite3DbFree(db, pIdxInfo);
+  return rc;
+}
+#endif /* SQLITE_OMIT_VIRTUALTABLE */
+
+/*
+** Add WhereLoop entries to handle OR terms.  This works for either
+** btrees or virtual tables.
+*/
+static int whereLoopAddOr(WhereLoopBuilder *pBuilder, Bitmask mExtra){
+  WhereInfo *pWInfo = pBuilder->pWInfo;
+  WhereClause *pWC;
+  WhereLoop *pNew;
+  WhereTerm *pTerm, *pWCEnd;
+  int rc = SQLITE_OK;
+  int iCur;
+  WhereClause tempWC;
+  WhereLoopBuilder sSubBuild;
+  WhereOrSet sSum, sCur;
+  struct SrcList_item *pItem;
+  
+  pWC = pBuilder->pWC;
+  pWCEnd = pWC->a + pWC->nTerm;
+  pNew = pBuilder->pNew;
+  memset(&sSum, 0, sizeof(sSum));
+  pItem = pWInfo->pTabList->a + pNew->iTab;
+  iCur = pItem->iCursor;
+
+  for(pTerm=pWC->a; pTerm<pWCEnd && rc==SQLITE_OK; pTerm++){
+    if( (pTerm->eOperator & WO_OR)!=0
+     && (pTerm->u.pOrInfo->indexable & pNew->maskSelf)!=0 
+    ){
+      WhereClause * const pOrWC = &pTerm->u.pOrInfo->wc;
+      WhereTerm * const pOrWCEnd = &pOrWC->a[pOrWC->nTerm];
+      WhereTerm *pOrTerm;
+      int once = 1;
+      int i, j;
+    
+      sSubBuild = *pBuilder;
+      sSubBuild.pOrderBy = 0;
+      sSubBuild.pOrSet = &sCur;
+
+      WHERETRACE(0x200, ("Begin processing OR-clause %p\n", pTerm));
+      for(pOrTerm=pOrWC->a; pOrTerm<pOrWCEnd; pOrTerm++){
+        if( (pOrTerm->eOperator & WO_AND)!=0 ){
+          sSubBuild.pWC = &pOrTerm->u.pAndInfo->wc;
+        }else if( pOrTerm->leftCursor==iCur ){
+          tempWC.pWInfo = pWC->pWInfo;
+          tempWC.pOuter = pWC;
+          tempWC.op = TK_AND;
+          tempWC.nTerm = 1;
+          tempWC.a = pOrTerm;
+          sSubBuild.pWC = &tempWC;
+        }else{
+          continue;
+        }
+        sCur.n = 0;
+#ifdef WHERETRACE_ENABLED
+        WHERETRACE(0x200, ("OR-term %d of %p has %d subterms:\n", 
+                   (int)(pOrTerm-pOrWC->a), pTerm, sSubBuild.pWC->nTerm));
+        if( sqlite3WhereTrace & 0x400 ){
+          for(i=0; i<sSubBuild.pWC->nTerm; i++){
+            whereTermPrint(&sSubBuild.pWC->a[i], i);
+          }
+        }
+#endif
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+        if( IsVirtual(pItem->pTab) ){
+          rc = whereLoopAddVirtual(&sSubBuild, mExtra);
+        }else
+#endif
+        {
+          rc = whereLoopAddBtree(&sSubBuild, mExtra);
+        }
+        if( rc==SQLITE_OK ){
+          rc = whereLoopAddOr(&sSubBuild, mExtra);
+        }
+        assert( rc==SQLITE_OK || sCur.n==0 );
+        if( sCur.n==0 ){
+          sSum.n = 0;
+          break;
+        }else if( once ){
+          whereOrMove(&sSum, &sCur);
+          once = 0;
+        }else{
+          WhereOrSet sPrev;
+          whereOrMove(&sPrev, &sSum);
+          sSum.n = 0;
+          for(i=0; i<sPrev.n; i++){
+            for(j=0; j<sCur.n; j++){
+              whereOrInsert(&sSum, sPrev.a[i].prereq | sCur.a[j].prereq,
+                            sqlite3LogEstAdd(sPrev.a[i].rRun, sCur.a[j].rRun),
+                            sqlite3LogEstAdd(sPrev.a[i].nOut, sCur.a[j].nOut));
+            }
+          }
+        }
+      }
+      pNew->nLTerm = 1;
+      pNew->aLTerm[0] = pTerm;
+      pNew->wsFlags = WHERE_MULTI_OR;
+      pNew->rSetup = 0;
+      pNew->iSortIdx = 0;
+      memset(&pNew->u, 0, sizeof(pNew->u));
+      for(i=0; rc==SQLITE_OK && i<sSum.n; i++){
+        /* TUNING: Currently sSum.a[i].rRun is set to the sum of the costs
+        ** of all sub-scans required by the OR-scan. However, due to rounding
+        ** errors, it may be that the cost of the OR-scan is equal to its
+        ** most expensive sub-scan. Add the smallest possible penalty 
+        ** (equivalent to multiplying the cost by 1.07) to ensure that 
+        ** this does not happen. Otherwise, for WHERE clauses such as the
+        ** following where there is an index on "y":
+        **
+        **     WHERE likelihood(x=?, 0.99) OR y=?
+        **
+        ** the planner may elect to "OR" together a full-table scan and an
+        ** index lookup. And other similarly odd results.  */
+        pNew->rRun = sSum.a[i].rRun + 1;
+        pNew->nOut = sSum.a[i].nOut;
+        pNew->prereq = sSum.a[i].prereq;
+        rc = whereLoopInsert(pBuilder, pNew);
+      }
+      WHERETRACE(0x200, ("End processing OR-clause %p\n", pTerm));
+    }
+  }
+  return rc;
+}
+
+/*
+** Add all WhereLoop objects for all tables 
+*/
+static int whereLoopAddAll(WhereLoopBuilder *pBuilder){
+  WhereInfo *pWInfo = pBuilder->pWInfo;
+  Bitmask mExtra = 0;
+  Bitmask mPrior = 0;
+  int iTab;
+  SrcList *pTabList = pWInfo->pTabList;
+  struct SrcList_item *pItem;
+  sqlite3 *db = pWInfo->pParse->db;
+  int nTabList = pWInfo->nLevel;
+  int rc = SQLITE_OK;
+  u8 priorJoinType = 0;
+  WhereLoop *pNew;
+
+  /* Loop over the tables in the join, from left to right */
+  pNew = pBuilder->pNew;
+  whereLoopInit(pNew);
+  for(iTab=0, pItem=pTabList->a; iTab<nTabList; iTab++, pItem++){
+    pNew->iTab = iTab;
+    pNew->maskSelf = getMask(&pWInfo->sMaskSet, pItem->iCursor);
+    if( ((pItem->jointype|priorJoinType) & (JT_LEFT|JT_CROSS))!=0 ){
+      mExtra = mPrior;
+    }
+    priorJoinType = pItem->jointype;
+    if( IsVirtual(pItem->pTab) ){
+      rc = whereLoopAddVirtual(pBuilder, mExtra);
+    }else{
+      rc = whereLoopAddBtree(pBuilder, mExtra);
+    }
+    if( rc==SQLITE_OK ){
+      rc = whereLoopAddOr(pBuilder, mExtra);
+    }
+    mPrior |= pNew->maskSelf;
+    if( rc || db->mallocFailed ) break;
+  }
+  whereLoopClear(db, pNew);
+  return rc;
+}
+
+/*
+** Examine a WherePath (with the addition of the extra WhereLoop of the 5th
+** parameters) to see if it outputs rows in the requested ORDER BY
+** (or GROUP BY) without requiring a separate sort operation.  Return N:
+** 
+**   N>0:   N terms of the ORDER BY clause are satisfied
+**   N==0:  No terms of the ORDER BY clause are satisfied
+**   N<0:   Unknown yet how many terms of ORDER BY might be satisfied.   
+**
+** Note that processing for WHERE_GROUPBY and WHERE_DISTINCTBY is not as
+** strict.  With GROUP BY and DISTINCT the only requirement is that
+** equivalent rows appear immediately adjacent to one another.  GROUP BY
+** and DISTINCT do not require rows to appear in any particular order as long
+** as equivalent rows are grouped together.  Thus for GROUP BY and DISTINCT
+** the pOrderBy terms can be matched in any order.  With ORDER BY, the 
+** pOrderBy terms must be matched in strict left-to-right order.
+*/
+static i8 wherePathSatisfiesOrderBy(
+  WhereInfo *pWInfo,    /* The WHERE clause */
+  ExprList *pOrderBy,   /* ORDER BY or GROUP BY or DISTINCT clause to check */
+  WherePath *pPath,     /* The WherePath to check */
+  u16 wctrlFlags,       /* Might contain WHERE_GROUPBY or WHERE_DISTINCTBY */
+  u16 nLoop,            /* Number of entries in pPath->aLoop[] */
+  WhereLoop *pLast,     /* Add this WhereLoop to the end of pPath->aLoop[] */
+  Bitmask *pRevMask     /* OUT: Mask of WhereLoops to run in reverse order */
+){
+  u8 revSet;            /* True if rev is known */
+  u8 rev;               /* Composite sort order */
+  u8 revIdx;            /* Index sort order */
+  u8 isOrderDistinct;   /* All prior WhereLoops are order-distinct */
+  u8 distinctColumns;   /* True if the loop has UNIQUE NOT NULL columns */
+  u8 isMatch;           /* iColumn matches a term of the ORDER BY clause */
+  u16 nKeyCol;          /* Number of key columns in pIndex */
+  u16 nColumn;          /* Total number of ordered columns in the index */
+  u16 nOrderBy;         /* Number terms in the ORDER BY clause */
+  int iLoop;            /* Index of WhereLoop in pPath being processed */
+  int i, j;             /* Loop counters */
+  int iCur;             /* Cursor number for current WhereLoop */
+  int iColumn;          /* A column number within table iCur */
+  WhereLoop *pLoop = 0; /* Current WhereLoop being processed. */
+  WhereTerm *pTerm;     /* A single term of the WHERE clause */
+  Expr *pOBExpr;        /* An expression from the ORDER BY clause */
+  CollSeq *pColl;       /* COLLATE function from an ORDER BY clause term */
+  Index *pIndex;        /* The index associated with pLoop */
+  sqlite3 *db = pWInfo->pParse->db;  /* Database connection */
+  Bitmask obSat = 0;    /* Mask of ORDER BY terms satisfied so far */
+  Bitmask obDone;       /* Mask of all ORDER BY terms */
+  Bitmask orderDistinctMask;  /* Mask of all well-ordered loops */
+  Bitmask ready;              /* Mask of inner loops */
+
+  /*
+  ** We say the WhereLoop is "one-row" if it generates no more than one
+  ** row of output.  A WhereLoop is one-row if all of the following are true:
+  **  (a) All index columns match with WHERE_COLUMN_EQ.
+  **  (b) The index is unique
+  ** Any WhereLoop with an WHERE_COLUMN_EQ constraint on the rowid is one-row.
+  ** Every one-row WhereLoop will have the WHERE_ONEROW bit set in wsFlags.
+  **
+  ** We say the WhereLoop is "order-distinct" if the set of columns from
+  ** that WhereLoop that are in the ORDER BY clause are different for every
+  ** row of the WhereLoop.  Every one-row WhereLoop is automatically
+  ** order-distinct.   A WhereLoop that has no columns in the ORDER BY clause
+  ** is not order-distinct. To be order-distinct is not quite the same as being
+  ** UNIQUE since a UNIQUE column or index can have multiple rows that 
+  ** are NULL and NULL values are equivalent for the purpose of order-distinct.
+  ** To be order-distinct, the columns must be UNIQUE and NOT NULL.
+  **
+  ** The rowid for a table is always UNIQUE and NOT NULL so whenever the
+  ** rowid appears in the ORDER BY clause, the corresponding WhereLoop is
+  ** automatically order-distinct.
+  */
+
+  assert( pOrderBy!=0 );
+  if( nLoop && OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ) return 0;
+
+  nOrderBy = pOrderBy->nExpr;
+  testcase( nOrderBy==BMS-1 );
+  if( nOrderBy>BMS-1 ) return 0;  /* Cannot optimize overly large ORDER BYs */
+  isOrderDistinct = 1;
+  obDone = MASKBIT(nOrderBy)-1;
+  orderDistinctMask = 0;
+  ready = 0;
+  for(iLoop=0; isOrderDistinct && obSat<obDone && iLoop<=nLoop; iLoop++){
+    if( iLoop>0 ) ready |= pLoop->maskSelf;
+    pLoop = iLoop<nLoop ? pPath->aLoop[iLoop] : pLast;
+    if( pLoop->wsFlags & WHERE_VIRTUALTABLE ){
+      if( pLoop->u.vtab.isOrdered ) obSat = obDone;
+      break;
+    }
+    iCur = pWInfo->pTabList->a[pLoop->iTab].iCursor;
+
+    /* Mark off any ORDER BY term X that is a column in the table of
+    ** the current loop for which there is term in the WHERE
+    ** clause of the form X IS NULL or X=? that reference only outer
+    ** loops.
+    */
+    for(i=0; i<nOrderBy; i++){
+      if( MASKBIT(i) & obSat ) continue;
+      pOBExpr = sqlite3ExprSkipCollate(pOrderBy->a[i].pExpr);
+      if( pOBExpr->op!=TK_COLUMN ) continue;
+      if( pOBExpr->iTable!=iCur ) continue;
+      pTerm = findTerm(&pWInfo->sWC, iCur, pOBExpr->iColumn,
+                       ~ready, WO_EQ|WO_ISNULL, 0);
+      if( pTerm==0 ) continue;
+      if( (pTerm->eOperator&WO_EQ)!=0 && pOBExpr->iColumn>=0 ){
+        const char *z1, *z2;
+        pColl = sqlite3ExprCollSeq(pWInfo->pParse, pOrderBy->a[i].pExpr);
+        if( !pColl ) pColl = db->pDfltColl;
+        z1 = pColl->zName;
+        pColl = sqlite3ExprCollSeq(pWInfo->pParse, pTerm->pExpr);
+        if( !pColl ) pColl = db->pDfltColl;
+        z2 = pColl->zName;
+        if( sqlite3StrICmp(z1, z2)!=0 ) continue;
+      }
+      obSat |= MASKBIT(i);
+    }
+
+    if( (pLoop->wsFlags & WHERE_ONEROW)==0 ){
+      if( pLoop->wsFlags & WHERE_IPK ){
+        pIndex = 0;
+        nKeyCol = 0;
+        nColumn = 1;
+      }else if( (pIndex = pLoop->u.btree.pIndex)==0 || pIndex->bUnordered ){
+        return 0;
+      }else{
+        nKeyCol = pIndex->nKeyCol;
+        nColumn = pIndex->nColumn;
+        assert( nColumn==nKeyCol+1 || !HasRowid(pIndex->pTable) );
+        assert( pIndex->aiColumn[nColumn-1]==(-1) || !HasRowid(pIndex->pTable));
+        isOrderDistinct = IsUniqueIndex(pIndex);
+      }
+
+      /* Loop through all columns of the index and deal with the ones
+      ** that are not constrained by == or IN.
+      */
+      rev = revSet = 0;
+      distinctColumns = 0;
+      for(j=0; j<nColumn; j++){
+        u8 bOnce;   /* True to run the ORDER BY search loop */
+
+        /* Skip over == and IS NULL terms */
+        if( j<pLoop->u.btree.nEq
+         && pLoop->u.btree.nSkip==0
+         && ((i = pLoop->aLTerm[j]->eOperator) & (WO_EQ|WO_ISNULL))!=0
+        ){
+          if( i & WO_ISNULL ){
+            testcase( isOrderDistinct );
+            isOrderDistinct = 0;
+          }
+          continue;  
+        }
+
+        /* Get the column number in the table (iColumn) and sort order
+        ** (revIdx) for the j-th column of the index.
+        */
+        if( pIndex ){
+          iColumn = pIndex->aiColumn[j];
+          revIdx = pIndex->aSortOrder[j];
+          if( iColumn==pIndex->pTable->iPKey ) iColumn = -1;
+        }else{
+          iColumn = -1;
+          revIdx = 0;
+        }
+
+        /* An unconstrained column that might be NULL means that this
+        ** WhereLoop is not well-ordered
+        */
+        if( isOrderDistinct
+         && iColumn>=0
+         && j>=pLoop->u.btree.nEq
+         && pIndex->pTable->aCol[iColumn].notNull==0
+        ){
+          isOrderDistinct = 0;
+        }
+
+        /* Find the ORDER BY term that corresponds to the j-th column
+        ** of the index and mark that ORDER BY term off 
+        */
+        bOnce = 1;
+        isMatch = 0;
+        for(i=0; bOnce && i<nOrderBy; i++){
+          if( MASKBIT(i) & obSat ) continue;
+          pOBExpr = sqlite3ExprSkipCollate(pOrderBy->a[i].pExpr);
+          testcase( wctrlFlags & WHERE_GROUPBY );
+          testcase( wctrlFlags & WHERE_DISTINCTBY );
+          if( (wctrlFlags & (WHERE_GROUPBY|WHERE_DISTINCTBY))==0 ) bOnce = 0;
+          if( pOBExpr->op!=TK_COLUMN ) continue;
+          if( pOBExpr->iTable!=iCur ) continue;
+          if( pOBExpr->iColumn!=iColumn ) continue;
+          if( iColumn>=0 ){
+            pColl = sqlite3ExprCollSeq(pWInfo->pParse, pOrderBy->a[i].pExpr);
+            if( !pColl ) pColl = db->pDfltColl;
+            if( sqlite3StrICmp(pColl->zName, pIndex->azColl[j])!=0 ) continue;
+          }
+          isMatch = 1;
+          break;
+        }
+        if( isMatch && (wctrlFlags & WHERE_GROUPBY)==0 ){
+          /* Make sure the sort order is compatible in an ORDER BY clause.
+          ** Sort order is irrelevant for a GROUP BY clause. */
+          if( revSet ){
+            if( (rev ^ revIdx)!=pOrderBy->a[i].sortOrder ) isMatch = 0;
+          }else{
+            rev = revIdx ^ pOrderBy->a[i].sortOrder;
+            if( rev ) *pRevMask |= MASKBIT(iLoop);
+            revSet = 1;
+          }
+        }
+        if( isMatch ){
+          if( iColumn<0 ){
+            testcase( distinctColumns==0 );
+            distinctColumns = 1;
+          }
+          obSat |= MASKBIT(i);
+        }else{
+          /* No match found */
+          if( j==0 || j<nKeyCol ){
+            testcase( isOrderDistinct!=0 );
+            isOrderDistinct = 0;
+          }
+          break;
+        }
+      } /* end Loop over all index columns */
+      if( distinctColumns ){
+        testcase( isOrderDistinct==0 );
+        isOrderDistinct = 1;
+      }
+    } /* end-if not one-row */
+
+    /* Mark off any other ORDER BY terms that reference pLoop */
+    if( isOrderDistinct ){
+      orderDistinctMask |= pLoop->maskSelf;
+      for(i=0; i<nOrderBy; i++){
+        Expr *p;
+        Bitmask mTerm;
+        if( MASKBIT(i) & obSat ) continue;
+        p = pOrderBy->a[i].pExpr;
+        mTerm = exprTableUsage(&pWInfo->sMaskSet,p);
+        if( mTerm==0 && !sqlite3ExprIsConstant(p) ) continue;
+        if( (mTerm&~orderDistinctMask)==0 ){
+          obSat |= MASKBIT(i);
+        }
+      }
+    }
+  } /* End the loop over all WhereLoops from outer-most down to inner-most */
+  if( obSat==obDone ) return (i8)nOrderBy;
+  if( !isOrderDistinct ){
+    for(i=nOrderBy-1; i>0; i--){
+      Bitmask m = MASKBIT(i) - 1;
+      if( (obSat&m)==m ) return i;
+    }
+    return 0;
+  }
+  return -1;
+}
+
+
+/*
+** If the WHERE_GROUPBY flag is set in the mask passed to sqlite3WhereBegin(),
+** the planner assumes that the specified pOrderBy list is actually a GROUP
+** BY clause - and so any order that groups rows as required satisfies the
+** request.
+**
+** Normally, in this case it is not possible for the caller to determine
+** whether or not the rows are really being delivered in sorted order, or
+** just in some other order that provides the required grouping. However,
+** if the WHERE_SORTBYGROUP flag is also passed to sqlite3WhereBegin(), then
+** this function may be called on the returned WhereInfo object. It returns
+** true if the rows really will be sorted in the specified order, or false
+** otherwise.
+**
+** For example, assuming:
+**
+**   CREATE INDEX i1 ON t1(x, Y);
+**
+** then
+**
+**   SELECT * FROM t1 GROUP BY x,y ORDER BY x,y;   -- IsSorted()==1
+**   SELECT * FROM t1 GROUP BY y,x ORDER BY y,x;   -- IsSorted()==0
+*/
+int sqlite3WhereIsSorted(WhereInfo *pWInfo){
+  assert( pWInfo->wctrlFlags & WHERE_GROUPBY );
+  assert( pWInfo->wctrlFlags & WHERE_SORTBYGROUP );
+  return pWInfo->sorted;
+}
+
+#ifdef WHERETRACE_ENABLED
+/* For debugging use only: */
+static const char *wherePathName(WherePath *pPath, int nLoop, WhereLoop *pLast){
+  static char zName[65];
+  int i;
+  for(i=0; i<nLoop; i++){ zName[i] = pPath->aLoop[i]->cId; }
+  if( pLast ) zName[i++] = pLast->cId;
+  zName[i] = 0;
+  return zName;
+}
+#endif
+
+/*
+** Return the cost of sorting nRow rows, assuming that the keys have 
+** nOrderby columns and that the first nSorted columns are already in
+** order.
+*/
+static LogEst whereSortingCost(
+  WhereInfo *pWInfo,
+  LogEst nRow,
+  int nOrderBy,
+  int nSorted
+){
+  /* TUNING: Estimated cost of a full external sort, where N is 
+  ** the number of rows to sort is:
+  **
+  **   cost = (3.0 * N * log(N)).
+  ** 
+  ** Or, if the order-by clause has X terms but only the last Y 
+  ** terms are out of order, then block-sorting will reduce the 
+  ** sorting cost to:
+  **
+  **   cost = (3.0 * N * log(N)) * (Y/X)
+  **
+  ** The (Y/X) term is implemented using stack variable rScale
+  ** below.  */
+  LogEst rScale, rSortCost;
+  assert( nOrderBy>0 && 66==sqlite3LogEst(100) );
+  rScale = sqlite3LogEst((nOrderBy-nSorted)*100/nOrderBy) - 66;
+  rSortCost = nRow + estLog(nRow) + rScale + 16;
+
+  /* TUNING: The cost of implementing DISTINCT using a B-TREE is
+  ** similar but with a larger constant of proportionality. 
+  ** Multiply by an additional factor of 3.0.  */
+  if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){
+    rSortCost += 16;
+  }
+
+  return rSortCost;
+}
+
+/*
+** Given the list of WhereLoop objects at pWInfo->pLoops, this routine
+** attempts to find the lowest cost path that visits each WhereLoop
+** once.  This path is then loaded into the pWInfo->a[].pWLoop fields.
+**
+** Assume that the total number of output rows that will need to be sorted
+** will be nRowEst (in the 10*log2 representation).  Or, ignore sorting
+** costs if nRowEst==0.
+**
+** Return SQLITE_OK on success or SQLITE_NOMEM of a memory allocation
+** error occurs.
+*/
+static int wherePathSolver(WhereInfo *pWInfo, LogEst nRowEst){
+  int mxChoice;             /* Maximum number of simultaneous paths tracked */
+  int nLoop;                /* Number of terms in the join */
+  Parse *pParse;            /* Parsing context */
+  sqlite3 *db;              /* The database connection */
+  int iLoop;                /* Loop counter over the terms of the join */
+  int ii, jj;               /* Loop counters */
+  int mxI = 0;              /* Index of next entry to replace */
+  int nOrderBy;             /* Number of ORDER BY clause terms */
+  LogEst mxCost = 0;        /* Maximum cost of a set of paths */
+  LogEst mxUnsorted = 0;    /* Maximum unsorted cost of a set of path */
+  int nTo, nFrom;           /* Number of valid entries in aTo[] and aFrom[] */
+  WherePath *aFrom;         /* All nFrom paths at the previous level */
+  WherePath *aTo;           /* The nTo best paths at the current level */
+  WherePath *pFrom;         /* An element of aFrom[] that we are working on */
+  WherePath *pTo;           /* An element of aTo[] that we are working on */
+  WhereLoop *pWLoop;        /* One of the WhereLoop objects */
+  WhereLoop **pX;           /* Used to divy up the pSpace memory */
+  LogEst *aSortCost = 0;    /* Sorting and partial sorting costs */
+  char *pSpace;             /* Temporary memory used by this routine */
+  int nSpace;               /* Bytes of space allocated at pSpace */
+
+  pParse = pWInfo->pParse;
+  db = pParse->db;
+  nLoop = pWInfo->nLevel;
+  /* TUNING: For simple queries, only the best path is tracked.
+  ** For 2-way joins, the 5 best paths are followed.
+  ** For joins of 3 or more tables, track the 10 best paths */
+  mxChoice = (nLoop<=1) ? 1 : (nLoop==2 ? 5 : 10);
+  assert( nLoop<=pWInfo->pTabList->nSrc );
+  WHERETRACE(0x002, ("---- begin solver.  (nRowEst=%d)\n", nRowEst));
+
+  /* If nRowEst is zero and there is an ORDER BY clause, ignore it. In this
+  ** case the purpose of this call is to estimate the number of rows returned
+  ** by the overall query. Once this estimate has been obtained, the caller
+  ** will invoke this function a second time, passing the estimate as the
+  ** nRowEst parameter.  */
+  if( pWInfo->pOrderBy==0 || nRowEst==0 ){
+    nOrderBy = 0;
+  }else{
+    nOrderBy = pWInfo->pOrderBy->nExpr;
+  }
+
+  /* Allocate and initialize space for aTo, aFrom and aSortCost[] */
+  nSpace = (sizeof(WherePath)+sizeof(WhereLoop*)*nLoop)*mxChoice*2;
+  nSpace += sizeof(LogEst) * nOrderBy;
+  pSpace = sqlite3DbMallocRaw(db, nSpace);
+  if( pSpace==0 ) return SQLITE_NOMEM;
+  aTo = (WherePath*)pSpace;
+  aFrom = aTo+mxChoice;
+  memset(aFrom, 0, sizeof(aFrom[0]));
+  pX = (WhereLoop**)(aFrom+mxChoice);
+  for(ii=mxChoice*2, pFrom=aTo; ii>0; ii--, pFrom++, pX += nLoop){
+    pFrom->aLoop = pX;
+  }
+  if( nOrderBy ){
+    /* If there is an ORDER BY clause and it is not being ignored, set up
+    ** space for the aSortCost[] array. Each element of the aSortCost array
+    ** is either zero - meaning it has not yet been initialized - or the
+    ** cost of sorting nRowEst rows of data where the first X terms of
+    ** the ORDER BY clause are already in order, where X is the array 
+    ** index.  */
+    aSortCost = (LogEst*)pX;
+    memset(aSortCost, 0, sizeof(LogEst) * nOrderBy);
+  }
+  assert( aSortCost==0 || &pSpace[nSpace]==(char*)&aSortCost[nOrderBy] );
+  assert( aSortCost!=0 || &pSpace[nSpace]==(char*)pX );
+
+  /* Seed the search with a single WherePath containing zero WhereLoops.
+  **
+  ** TUNING: Do not let the number of iterations go above 25.  If the cost
+  ** of computing an automatic index is not paid back within the first 25
+  ** rows, then do not use the automatic index. */
+  aFrom[0].nRow = MIN(pParse->nQueryLoop, 46);  assert( 46==sqlite3LogEst(25) );
+  nFrom = 1;
+  assert( aFrom[0].isOrdered==0 );
+  if( nOrderBy ){
+    /* If nLoop is zero, then there are no FROM terms in the query. Since
+    ** in this case the query may return a maximum of one row, the results
+    ** are already in the requested order. Set isOrdered to nOrderBy to
+    ** indicate this. Or, if nLoop is greater than zero, set isOrdered to
+    ** -1, indicating that the result set may or may not be ordered, 
+    ** depending on the loops added to the current plan.  */
+    aFrom[0].isOrdered = nLoop>0 ? -1 : nOrderBy;
+  }
+
+  /* Compute successively longer WherePaths using the previous generation
+  ** of WherePaths as the basis for the next.  Keep track of the mxChoice
+  ** best paths at each generation */
+  for(iLoop=0; iLoop<nLoop; iLoop++){
+    nTo = 0;
+    for(ii=0, pFrom=aFrom; ii<nFrom; ii++, pFrom++){
+      for(pWLoop=pWInfo->pLoops; pWLoop; pWLoop=pWLoop->pNextLoop){
+        LogEst nOut;                      /* Rows visited by (pFrom+pWLoop) */
+        LogEst rCost;                     /* Cost of path (pFrom+pWLoop) */
+        LogEst rUnsorted;                 /* Unsorted cost of (pFrom+pWLoop) */
+        i8 isOrdered = pFrom->isOrdered;  /* isOrdered for (pFrom+pWLoop) */
+        Bitmask maskNew;                  /* Mask of src visited by (..) */
+        Bitmask revMask = 0;              /* Mask of rev-order loops for (..) */
+
+        if( (pWLoop->prereq & ~pFrom->maskLoop)!=0 ) continue;
+        if( (pWLoop->maskSelf & pFrom->maskLoop)!=0 ) continue;
+        /* At this point, pWLoop is a candidate to be the next loop. 
+        ** Compute its cost */
+        rUnsorted = sqlite3LogEstAdd(pWLoop->rSetup,pWLoop->rRun + pFrom->nRow);
+        rUnsorted = sqlite3LogEstAdd(rUnsorted, pFrom->rUnsorted);
+        nOut = pFrom->nRow + pWLoop->nOut;
+        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
+        if( isOrdered<0 ){
+          isOrdered = wherePathSatisfiesOrderBy(pWInfo,
+                       pWInfo->pOrderBy, pFrom, pWInfo->wctrlFlags,
+                       iLoop, pWLoop, &revMask);
+        }else{
+          revMask = pFrom->revLoop;
+        }
+        if( isOrdered>=0 && isOrdered<nOrderBy ){
+          if( aSortCost[isOrdered]==0 ){
+            aSortCost[isOrdered] = whereSortingCost(
+                pWInfo, nRowEst, nOrderBy, isOrdered
+            );
+          }
+          rCost = sqlite3LogEstAdd(rUnsorted, aSortCost[isOrdered]);
+
+          WHERETRACE(0x002,
+              ("---- sort cost=%-3d (%d/%d) increases cost %3d to %-3d\n",
+               aSortCost[isOrdered], (nOrderBy-isOrdered), nOrderBy, 
+               rUnsorted, rCost));
+        }else{
+          rCost = rUnsorted;
+        }
+
+        /* Check to see if pWLoop should be added to the set of
+        ** mxChoice best-so-far paths.
+        **
+        ** First look for an existing path among best-so-far paths
+        ** that covers the same set of loops and has the same isOrdered
+        ** setting as the current path candidate.
+        **
+        ** The term "((pTo->isOrdered^isOrdered)&0x80)==0" is equivalent
+        ** to (pTo->isOrdered==(-1))==(isOrdered==(-1))" for the range
+        ** of legal values for isOrdered, -1..64.
+        */
+        for(jj=0, pTo=aTo; jj<nTo; jj++, pTo++){
+          if( pTo->maskLoop==maskNew
+           && ((pTo->isOrdered^isOrdered)&0x80)==0
+          ){
+            testcase( jj==nTo-1 );
+            break;
+          }
+        }
+        if( jj>=nTo ){
+          /* None of the existing best-so-far paths match the candidate. */
+          if( nTo>=mxChoice
+           && (rCost>mxCost || (rCost==mxCost && rUnsorted>=mxUnsorted))
+          ){
+            /* The current candidate is no better than any of the mxChoice
+            ** paths currently in the best-so-far buffer.  So discard
+            ** this candidate as not viable. */
+#ifdef WHERETRACE_ENABLED /* 0x4 */
+            if( sqlite3WhereTrace&0x4 ){
+              sqlite3DebugPrintf("Skip   %s cost=%-3d,%3d order=%c\n",
+                  wherePathName(pFrom, iLoop, pWLoop), rCost, nOut,
+                  isOrdered>=0 ? isOrdered+'0' : '?');
+            }
+#endif
+            continue;
+          }
+          /* If we reach this points it means that the new candidate path
+          ** needs to be added to the set of best-so-far paths. */
+          if( nTo<mxChoice ){
+            /* Increase the size of the aTo set by one */
+            jj = nTo++;
+          }else{
+            /* New path replaces the prior worst to keep count below mxChoice */
+            jj = mxI;
+          }
+          pTo = &aTo[jj];
+#ifdef WHERETRACE_ENABLED /* 0x4 */
+          if( sqlite3WhereTrace&0x4 ){
+            sqlite3DebugPrintf("New    %s cost=%-3d,%3d order=%c\n",
+                wherePathName(pFrom, iLoop, pWLoop), rCost, nOut,
+                isOrdered>=0 ? isOrdered+'0' : '?');
+          }
+#endif
+        }else{
+          /* Control reaches here if best-so-far path pTo=aTo[jj] covers the
+          ** same set of loops and has the sam isOrdered setting as the
+          ** candidate path.  Check to see if the candidate should replace
+          ** pTo or if the candidate should be skipped */
+          if( pTo->rCost<rCost || (pTo->rCost==rCost && pTo->nRow<=nOut) ){
+#ifdef WHERETRACE_ENABLED /* 0x4 */
+            if( sqlite3WhereTrace&0x4 ){
+              sqlite3DebugPrintf(
+                  "Skip   %s cost=%-3d,%3d order=%c",
+                  wherePathName(pFrom, iLoop, pWLoop), rCost, nOut,
+                  isOrdered>=0 ? isOrdered+'0' : '?');
+              sqlite3DebugPrintf("   vs %s cost=%-3d,%d order=%c\n",
+                  wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
+                  pTo->isOrdered>=0 ? pTo->isOrdered+'0' : '?');
+            }
+#endif
+            /* Discard the candidate path from further consideration */
+            testcase( pTo->rCost==rCost );
+            continue;
+          }
+          testcase( pTo->rCost==rCost+1 );
+          /* Control reaches here if the candidate path is better than the
+          ** pTo path.  Replace pTo with the candidate. */
+#ifdef WHERETRACE_ENABLED /* 0x4 */
+          if( sqlite3WhereTrace&0x4 ){
+            sqlite3DebugPrintf(
+                "Update %s cost=%-3d,%3d order=%c",
+                wherePathName(pFrom, iLoop, pWLoop), rCost, nOut,
+                isOrdered>=0 ? isOrdered+'0' : '?');
+            sqlite3DebugPrintf("  was %s cost=%-3d,%3d order=%c\n",
+                wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
+                pTo->isOrdered>=0 ? pTo->isOrdered+'0' : '?');
+          }
+#endif
+        }
+        /* pWLoop is a winner.  Add it to the set of best so far */
+        pTo->maskLoop = pFrom->maskLoop | pWLoop->maskSelf;
+        pTo->revLoop = revMask;
+        pTo->nRow = nOut;
+        pTo->rCost = rCost;
+        pTo->rUnsorted = rUnsorted;
+        pTo->isOrdered = isOrdered;
+        memcpy(pTo->aLoop, pFrom->aLoop, sizeof(WhereLoop*)*iLoop);
+        pTo->aLoop[iLoop] = pWLoop;
+        if( nTo>=mxChoice ){
+          mxI = 0;
+          mxCost = aTo[0].rCost;
+          mxUnsorted = aTo[0].nRow;
+          for(jj=1, pTo=&aTo[1]; jj<mxChoice; jj++, pTo++){
+            if( pTo->rCost>mxCost 
+             || (pTo->rCost==mxCost && pTo->rUnsorted>mxUnsorted) 
+            ){
+              mxCost = pTo->rCost;
+              mxUnsorted = pTo->rUnsorted;
+              mxI = jj;
+            }
+          }
+        }
+      }
+    }
+
+#ifdef WHERETRACE_ENABLED  /* >=2 */
+    if( sqlite3WhereTrace>=2 ){
+      sqlite3DebugPrintf("---- after round %d ----\n", iLoop);
+      for(ii=0, pTo=aTo; ii<nTo; ii++, pTo++){
+        sqlite3DebugPrintf(" %s cost=%-3d nrow=%-3d order=%c",
+           wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
+           pTo->isOrdered>=0 ? (pTo->isOrdered+'0') : '?');
+        if( pTo->isOrdered>0 ){
+          sqlite3DebugPrintf(" rev=0x%llx\n", pTo->revLoop);
+        }else{
+          sqlite3DebugPrintf("\n");
+        }
+      }
+    }
+#endif
+
+    /* Swap the roles of aFrom and aTo for the next generation */
+    pFrom = aTo;
+    aTo = aFrom;
+    aFrom = pFrom;
+    nFrom = nTo;
+  }
+
+  if( nFrom==0 ){
+    sqlite3ErrorMsg(pParse, "no query solution");
+    sqlite3DbFree(db, pSpace);
+    return SQLITE_ERROR;
+  }
+  
+  /* Find the lowest cost path.  pFrom will be left pointing to that path */
+  pFrom = aFrom;
+  for(ii=1; ii<nFrom; ii++){
+    if( pFrom->rCost>aFrom[ii].rCost ) pFrom = &aFrom[ii];
+  }
+  assert( pWInfo->nLevel==nLoop );
+  /* Load the lowest cost path into pWInfo */
+  for(iLoop=0; iLoop<nLoop; iLoop++){
+    WhereLevel *pLevel = pWInfo->a + iLoop;
+    pLevel->pWLoop = pWLoop = pFrom->aLoop[iLoop];
+    pLevel->iFrom = pWLoop->iTab;
+    pLevel->iTabCur = pWInfo->pTabList->a[pLevel->iFrom].iCursor;
+  }
+  if( (pWInfo->wctrlFlags & WHERE_WANT_DISTINCT)!=0
+   && (pWInfo->wctrlFlags & WHERE_DISTINCTBY)==0
+   && pWInfo->eDistinct==WHERE_DISTINCT_NOOP
+   && nRowEst
+  ){
+    Bitmask notUsed;
+    int rc = wherePathSatisfiesOrderBy(pWInfo, pWInfo->pResultSet, pFrom,
+                 WHERE_DISTINCTBY, nLoop-1, pFrom->aLoop[nLoop-1], &notUsed);
+    if( rc==pWInfo->pResultSet->nExpr ){
+      pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;
+    }
+  }
+  if( pWInfo->pOrderBy ){
+    if( pWInfo->wctrlFlags & WHERE_DISTINCTBY ){
+      if( pFrom->isOrdered==pWInfo->pOrderBy->nExpr ){
+        pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;
+      }
+    }else{
+      pWInfo->nOBSat = pFrom->isOrdered;
+      if( pWInfo->nOBSat<0 ) pWInfo->nOBSat = 0;
+      pWInfo->revMask = pFrom->revLoop;
+    }
+    if( (pWInfo->wctrlFlags & WHERE_SORTBYGROUP)
+        && pWInfo->nOBSat==pWInfo->pOrderBy->nExpr
+    ){
+      Bitmask revMask = 0;
+      int nOrder = wherePathSatisfiesOrderBy(pWInfo, pWInfo->pOrderBy, 
+          pFrom, 0, nLoop-1, pFrom->aLoop[nLoop-1], &revMask
+      );
+      assert( pWInfo->sorted==0 );
+      if( nOrder==pWInfo->pOrderBy->nExpr ){
+        pWInfo->sorted = 1;
+        pWInfo->revMask = revMask;
+      }
+    }
+  }
+
+
+  pWInfo->nRowOut = pFrom->nRow;
+
+  /* Free temporary memory and return success */
+  sqlite3DbFree(db, pSpace);
+  return SQLITE_OK;
+}
+
+/*
+** Most queries use only a single table (they are not joins) and have
+** simple == constraints against indexed fields.  This routine attempts
+** to plan those simple cases using much less ceremony than the
+** general-purpose query planner, and thereby yield faster sqlite3_prepare()
+** times for the common case.
+**
+** Return non-zero on success, if this query can be handled by this
+** no-frills query planner.  Return zero if this query needs the 
+** general-purpose query planner.
+*/
+static int whereShortCut(WhereLoopBuilder *pBuilder){
+  WhereInfo *pWInfo;
+  struct SrcList_item *pItem;
+  WhereClause *pWC;
+  WhereTerm *pTerm;
+  WhereLoop *pLoop;
+  int iCur;
+  int j;
+  Table *pTab;
+  Index *pIdx;
+  
+  pWInfo = pBuilder->pWInfo;
+  if( pWInfo->wctrlFlags & WHERE_FORCE_TABLE ) return 0;
+  assert( pWInfo->pTabList->nSrc>=1 );
+  pItem = pWInfo->pTabList->a;
+  pTab = pItem->pTab;
+  if( IsVirtual(pTab) ) return 0;
+  if( pItem->zIndex ) return 0;
+  iCur = pItem->iCursor;
+  pWC = &pWInfo->sWC;
+  pLoop = pBuilder->pNew;
+  pLoop->wsFlags = 0;
+  pLoop->u.btree.nSkip = 0;
+  pTerm = findTerm(pWC, iCur, -1, 0, WO_EQ, 0);
+  if( pTerm ){
+    pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_IPK|WHERE_ONEROW;
+    pLoop->aLTerm[0] = pTerm;
+    pLoop->nLTerm = 1;
+    pLoop->u.btree.nEq = 1;
+    /* TUNING: Cost of a rowid lookup is 10 */
+    pLoop->rRun = 33;  /* 33==sqlite3LogEst(10) */
+  }else{
+    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
+      assert( pLoop->aLTermSpace==pLoop->aLTerm );
+      assert( ArraySize(pLoop->aLTermSpace)==4 );
+      if( !IsUniqueIndex(pIdx)
+       || pIdx->pPartIdxWhere!=0 
+       || pIdx->nKeyCol>ArraySize(pLoop->aLTermSpace) 
+      ) continue;
+      for(j=0; j<pIdx->nKeyCol; j++){
+        pTerm = findTerm(pWC, iCur, pIdx->aiColumn[j], 0, WO_EQ, pIdx);
+        if( pTerm==0 ) break;
+        pLoop->aLTerm[j] = pTerm;
+      }
+      if( j!=pIdx->nKeyCol ) continue;
+      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;
+      if( pIdx->isCovering || (pItem->colUsed & ~columnsInIndex(pIdx))==0 ){
+        pLoop->wsFlags |= WHERE_IDX_ONLY;
+      }
+      pLoop->nLTerm = j;
+      pLoop->u.btree.nEq = j;
+      pLoop->u.btree.pIndex = pIdx;
+      /* TUNING: Cost of a unique index lookup is 15 */
+      pLoop->rRun = 39;  /* 39==sqlite3LogEst(15) */
+      break;
+    }
+  }
+  if( pLoop->wsFlags ){
+    pLoop->nOut = (LogEst)1;
+    pWInfo->a[0].pWLoop = pLoop;
+    pLoop->maskSelf = getMask(&pWInfo->sMaskSet, iCur);
+    pWInfo->a[0].iTabCur = iCur;
+    pWInfo->nRowOut = 1;
+    if( pWInfo->pOrderBy ) pWInfo->nOBSat =  pWInfo->pOrderBy->nExpr;
+    if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){
+      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
+    }
+#ifdef SQLITE_DEBUG
+    pLoop->cId = '0';
+#endif
+    return 1;
+  }
+  return 0;
+}
+
+/*
+** 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
+**
+** pOrderBy is a pointer to the ORDER BY clause (or the GROUP BY clause
+** if the WHERE_GROUPBY flag is set in wctrlFlags) 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 pOrderBy is NULL.
+**
+** The iIdxCur parameter is the cursor number of an index.  If 
+** WHERE_ONETABLE_ONLY is set, iIdxCur is the cursor number of an index
+** to use for OR clause processing.  The WHERE clause should use this
+** specific cursor.  If WHERE_ONEPASS_DESIRED is set, then iIdxCur is
+** the first cursor in an array of cursors for all indices.  iIdxCur should
+** be used to compute the appropriate cursor depending on which index is
+** used.
+*/
+WhereInfo *sqlite3WhereBegin(
+  Parse *pParse,        /* The parser context */
+  SrcList *pTabList,    /* FROM clause: A list of all tables to be scanned */
+  Expr *pWhere,         /* The WHERE clause */
+  ExprList *pOrderBy,   /* An ORDER BY (or GROUP BY) clause, or NULL */
+  ExprList *pResultSet, /* Result set of the query */
+  u16 wctrlFlags,       /* One of the WHERE_* flags defined in sqliteInt.h */
+  int iIdxCur           /* If WHERE_ONETABLE_ONLY is set, index cursor number */
+){
+  int nByteWInfo;            /* Num. bytes allocated for WhereInfo struct */
+  int nTabList;              /* Number of elements in pTabList */
+  WhereInfo *pWInfo;         /* Will become the return value of this function */
+  Vdbe *v = pParse->pVdbe;   /* The virtual database engine */
+  Bitmask notReady;          /* Cursors that are not yet positioned */
+  WhereLoopBuilder sWLB;     /* The WhereLoop builder */
+  WhereMaskSet *pMaskSet;    /* The expression mask set */
+  WhereLevel *pLevel;        /* A single level in pWInfo->a[] */
+  WhereLoop *pLoop;          /* Pointer to a single WhereLoop object */
+  int ii;                    /* Loop counter */
+  sqlite3 *db;               /* Database connection */
+  int rc;                    /* Return code */
+
+
+  /* Variable initialization */
+  db = pParse->db;
+  memset(&sWLB, 0, sizeof(sWLB));
+
+  /* An ORDER/GROUP BY clause of more than 63 terms cannot be optimized */
+  testcase( pOrderBy && pOrderBy->nExpr==BMS-1 );
+  if( pOrderBy && pOrderBy->nExpr>=BMS ) pOrderBy = 0;
+  sWLB.pOrderBy = pOrderBy;
+
+  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via
+  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */
+  if( OptimizationDisabled(db, SQLITE_DistinctOpt) ){
+    wctrlFlags &= ~WHERE_WANT_DISTINCT;
+  }
+
+  /* The number of tables in the FROM clause is limited by the number of
+  ** bits in a Bitmask 
+  */
+  testcase( pTabList->nSrc==BMS );
+  if( pTabList->nSrc>BMS ){
+    sqlite3ErrorMsg(pParse, "at most %d tables in a join", BMS);
+    return 0;
+  }
+
+  /* This function normally generates a nested loop for all tables in 
+  ** pTabList.  But if the WHERE_ONETABLE_ONLY flag is set, then we should
+  ** only generate code for the first table in pTabList and assume that
+  ** any cursors associated with subsequent tables are uninitialized.
+  */
+  nTabList = (wctrlFlags & WHERE_ONETABLE_ONLY) ? 1 : pTabList->nSrc;
+
+  /* Allocate and initialize the WhereInfo structure that will become the
+  ** return value. A single allocation is used to store the WhereInfo
+  ** struct, the contents of WhereInfo.a[], the WhereClause structure
+  ** and the WhereMaskSet structure. Since WhereClause contains an 8-byte
+  ** field (type Bitmask) it must be aligned on an 8-byte boundary on
+  ** some architectures. Hence the ROUND8() below.
+  */
+  nByteWInfo = ROUND8(sizeof(WhereInfo)+(nTabList-1)*sizeof(WhereLevel));
+  pWInfo = sqlite3DbMallocZero(db, nByteWInfo + sizeof(WhereLoop));
+  if( db->mallocFailed ){
+    sqlite3DbFree(db, pWInfo);
+    pWInfo = 0;
+    goto whereBeginError;
+  }
+  pWInfo->aiCurOnePass[0] = pWInfo->aiCurOnePass[1] = -1;
+  pWInfo->nLevel = nTabList;
+  pWInfo->pParse = pParse;
+  pWInfo->pTabList = pTabList;
+  pWInfo->pOrderBy = pOrderBy;
+  pWInfo->pResultSet = pResultSet;
+  pWInfo->iBreak = pWInfo->iContinue = sqlite3VdbeMakeLabel(v);
+  pWInfo->wctrlFlags = wctrlFlags;
+  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
+  pMaskSet = &pWInfo->sMaskSet;
+  sWLB.pWInfo = pWInfo;
+  sWLB.pWC = &pWInfo->sWC;
+  sWLB.pNew = (WhereLoop*)(((char*)pWInfo)+nByteWInfo);
+  assert( EIGHT_BYTE_ALIGNMENT(sWLB.pNew) );
+  whereLoopInit(sWLB.pNew);
+#ifdef SQLITE_DEBUG
+  sWLB.pNew->cId = '*';
+#endif
+
+  /* Split the WHERE clause into separate subexpressions where each
+  ** subexpression is separated by an AND operator.
+  */
+  initMaskSet(pMaskSet);
+  whereClauseInit(&pWInfo->sWC, pWInfo);
+  whereSplit(&pWInfo->sWC, pWhere, TK_AND);
+    
+  /* Special case: a WHERE clause that is constant.  Evaluate the
+  ** expression and either jump over all of the code or fall thru.
+  */
+  for(ii=0; ii<sWLB.pWC->nTerm; ii++){
+    if( nTabList==0 || sqlite3ExprIsConstantNotJoin(sWLB.pWC->a[ii].pExpr) ){
+      sqlite3ExprIfFalse(pParse, sWLB.pWC->a[ii].pExpr, pWInfo->iBreak,
+                         SQLITE_JUMPIFNULL);
+      sWLB.pWC->a[ii].wtFlags |= TERM_CODED;
+    }
+  }
+
+  /* Special case: No FROM clause
+  */
+  if( nTabList==0 ){
+    if( pOrderBy ) pWInfo->nOBSat = pOrderBy->nExpr;
+    if( wctrlFlags & WHERE_WANT_DISTINCT ){
+      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
+    }
+  }
+
+  /* Assign a bit from the bitmask to every term in the FROM clause.
+  **
+  ** When assigning bitmask values to FROM clause cursors, it must be
+  ** the case that if X is the bitmask for the N-th FROM clause term then
+  ** the bitmask for all FROM clause terms to the left of the N-th term
+  ** is (X-1).   An expression from the ON clause of a LEFT JOIN can use
+  ** its Expr.iRightJoinTable value to find the bitmask of the right table
+  ** of the join.  Subtracting one from the right table bitmask gives a
+  ** bitmask for all tables to the left of the join.  Knowing the bitmask
+  ** for all tables to the left of a left join is important.  Ticket #3015.
+  **
+  ** Note that bitmasks are created for all pTabList->nSrc tables in
+  ** pTabList, not just the first nTabList tables.  nTabList is normally
+  ** equal to pTabList->nSrc but might be shortened to 1 if the
+  ** WHERE_ONETABLE_ONLY flag is set.
+  */
+  for(ii=0; ii<pTabList->nSrc; ii++){
+    createMask(pMaskSet, pTabList->a[ii].iCursor);
+  }
+#ifndef NDEBUG
+  {
+    Bitmask toTheLeft = 0;
+    for(ii=0; ii<pTabList->nSrc; ii++){
+      Bitmask m = getMask(pMaskSet, pTabList->a[ii].iCursor);
+      assert( (m-1)==toTheLeft );
+      toTheLeft |= m;
+    }
+  }
+#endif
+
+  /* Analyze all of the subexpressions.  Note that exprAnalyze() might
+  ** add new virtual terms onto the end of the WHERE clause.  We do not
+  ** want to analyze these virtual terms, so start analyzing at the end
+  ** and work forward so that the added virtual terms are never processed.
+  */
+  exprAnalyzeAll(pTabList, &pWInfo->sWC);
+  if( db->mallocFailed ){
+    goto whereBeginError;
+  }
+
+  if( wctrlFlags & WHERE_WANT_DISTINCT ){
+    if( isDistinctRedundant(pParse, pTabList, &pWInfo->sWC, pResultSet) ){
+      /* The DISTINCT marking is pointless.  Ignore it. */
+      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
+    }else if( pOrderBy==0 ){
+      /* Try to ORDER BY the result set to make distinct processing easier */
+      pWInfo->wctrlFlags |= WHERE_DISTINCTBY;
+      pWInfo->pOrderBy = pResultSet;
+    }
+  }
+
+  /* Construct the WhereLoop objects */
+  WHERETRACE(0xffff,("*** Optimizer Start ***\n"));
+#if defined(WHERETRACE_ENABLED)
+  /* Display all terms of the WHERE clause */
+  if( sqlite3WhereTrace & 0x100 ){
+    int i;
+    for(i=0; i<sWLB.pWC->nTerm; i++){
+      whereTermPrint(&sWLB.pWC->a[i], i);
+    }
+  }
+#endif
+
+  if( nTabList!=1 || whereShortCut(&sWLB)==0 ){
+    rc = whereLoopAddAll(&sWLB);
+    if( rc ) goto whereBeginError;
+  
+    /* Display all of the WhereLoop objects if wheretrace is enabled */
+#ifdef WHERETRACE_ENABLED /* !=0 */
+    if( sqlite3WhereTrace ){
+      WhereLoop *p;
+      int i;
+      static char zLabel[] = "0123456789abcdefghijklmnopqrstuvwyxz"
+                                       "ABCDEFGHIJKLMNOPQRSTUVWYXZ";
+      for(p=pWInfo->pLoops, i=0; p; p=p->pNextLoop, i++){
+        p->cId = zLabel[i%sizeof(zLabel)];
+        whereLoopPrint(p, sWLB.pWC);
+      }
+    }
+#endif
+  
+    wherePathSolver(pWInfo, 0);
+    if( db->mallocFailed ) goto whereBeginError;
+    if( pWInfo->pOrderBy ){
+       wherePathSolver(pWInfo, pWInfo->nRowOut+1);
+       if( db->mallocFailed ) goto whereBeginError;
+    }
+  }
+  if( pWInfo->pOrderBy==0 && (db->flags & SQLITE_ReverseOrder)!=0 ){
+     pWInfo->revMask = (Bitmask)(-1);
+  }
+  if( pParse->nErr || NEVER(db->mallocFailed) ){
+    goto whereBeginError;
+  }
+#ifdef WHERETRACE_ENABLED /* !=0 */
+  if( sqlite3WhereTrace ){
+    int ii;
+    sqlite3DebugPrintf("---- Solution nRow=%d", pWInfo->nRowOut);
+    if( pWInfo->nOBSat>0 ){
+      sqlite3DebugPrintf(" ORDERBY=%d,0x%llx", pWInfo->nOBSat, pWInfo->revMask);
+    }
+    switch( pWInfo->eDistinct ){
+      case WHERE_DISTINCT_UNIQUE: {
+        sqlite3DebugPrintf("  DISTINCT=unique");
+        break;
+      }
+      case WHERE_DISTINCT_ORDERED: {
+        sqlite3DebugPrintf("  DISTINCT=ordered");
+        break;
+      }
+      case WHERE_DISTINCT_UNORDERED: {
+        sqlite3DebugPrintf("  DISTINCT=unordered");
+        break;
+      }
+    }
+    sqlite3DebugPrintf("\n");
+    for(ii=0; ii<pWInfo->nLevel; ii++){
+      whereLoopPrint(pWInfo->a[ii].pWLoop, sWLB.pWC);
+    }
+  }
+#endif
+  /* Attempt to omit tables from the join that do not effect the result */
+  if( pWInfo->nLevel>=2
+   && pResultSet!=0
+   && OptimizationEnabled(db, SQLITE_OmitNoopJoin)
+  ){
+    Bitmask tabUsed = exprListTableUsage(pMaskSet, pResultSet);
+    if( sWLB.pOrderBy ) tabUsed |= exprListTableUsage(pMaskSet, sWLB.pOrderBy);
+    while( pWInfo->nLevel>=2 ){
+      WhereTerm *pTerm, *pEnd;
+      pLoop = pWInfo->a[pWInfo->nLevel-1].pWLoop;
+      if( (pWInfo->pTabList->a[pLoop->iTab].jointype & JT_LEFT)==0 ) break;
+      if( (wctrlFlags & WHERE_WANT_DISTINCT)==0
+       && (pLoop->wsFlags & WHERE_ONEROW)==0
+      ){
+        break;
+      }
+      if( (tabUsed & pLoop->maskSelf)!=0 ) break;
+      pEnd = sWLB.pWC->a + sWLB.pWC->nTerm;
+      for(pTerm=sWLB.pWC->a; pTerm<pEnd; pTerm++){
+        if( (pTerm->prereqAll & pLoop->maskSelf)!=0
+         && !ExprHasProperty(pTerm->pExpr, EP_FromJoin)
+        ){
+          break;
+        }
+      }
+      if( pTerm<pEnd ) break;
+      WHERETRACE(0xffff, ("-> drop loop %c not used\n", pLoop->cId));
+      pWInfo->nLevel--;
+      nTabList--;
+    }
+  }
+  WHERETRACE(0xffff,("*** Optimizer Finished ***\n"));
+  pWInfo->pParse->nQueryLoop += pWInfo->nRowOut;
+
+  /* If the caller is an UPDATE or DELETE statement that is requesting
+  ** to use a one-pass algorithm, determine if this is appropriate.
+  ** The one-pass algorithm only works if the WHERE clause constrains
+  ** the statement to update a single row.
+  */
+  assert( (wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || pWInfo->nLevel==1 );
+  if( (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 
+   && (pWInfo->a[0].pWLoop->wsFlags & WHERE_ONEROW)!=0 ){
+    pWInfo->okOnePass = 1;
+    if( HasRowid(pTabList->a[0].pTab) ){
+      pWInfo->a[0].pWLoop->wsFlags &= ~WHERE_IDX_ONLY;
+    }
+  }
+
+  /* Open all tables in the pTabList and any indices selected for
+  ** searching those tables.
+  */
+  notReady = ~(Bitmask)0;
+  for(ii=0, pLevel=pWInfo->a; ii<nTabList; ii++, pLevel++){
+    Table *pTab;     /* Table to open */
+    int iDb;         /* Index of database containing table/index */
+    struct SrcList_item *pTabItem;
+
+    pTabItem = &pTabList->a[pLevel->iFrom];
+    pTab = pTabItem->pTab;
+    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);
+    pLoop = pLevel->pWLoop;
+    if( (pTab->tabFlags & TF_Ephemeral)!=0 || pTab->pSelect ){
+      /* Do nothing */
+    }else
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+    if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)!=0 ){
+      const char *pVTab = (const char *)sqlite3GetVTable(db, pTab);
+      int iCur = pTabItem->iCursor;
+      sqlite3VdbeAddOp4(v, OP_VOpen, iCur, 0, 0, pVTab, P4_VTAB);
+    }else if( IsVirtual(pTab) ){
+      /* noop */
+    }else
+#endif
+    if( (pLoop->wsFlags & WHERE_IDX_ONLY)==0
+         && (wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0 ){
+      int op = OP_OpenRead;
+      if( pWInfo->okOnePass ){
+        op = OP_OpenWrite;
+        pWInfo->aiCurOnePass[0] = pTabItem->iCursor;
+      };
+      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);
+      assert( pTabItem->iCursor==pLevel->iTabCur );
+      testcase( !pWInfo->okOnePass && pTab->nCol==BMS-1 );
+      testcase( !pWInfo->okOnePass && pTab->nCol==BMS );
+      if( !pWInfo->okOnePass && pTab->nCol<BMS && HasRowid(pTab) ){
+        Bitmask b = pTabItem->colUsed;
+        int n = 0;
+        for(; b; b=b>>1, n++){}
+        sqlite3VdbeChangeP4(v, sqlite3VdbeCurrentAddr(v)-1, 
+                            SQLITE_INT_TO_PTR(n), P4_INT32);
+        assert( n<=pTab->nCol );
+      }
+    }else{
+      sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);
+    }
+    if( pLoop->wsFlags & WHERE_INDEXED ){
+      Index *pIx = pLoop->u.btree.pIndex;
+      int iIndexCur;
+      int op = OP_OpenRead;
+      /* iIdxCur is always set if to a positive value if ONEPASS is possible */
+      assert( iIdxCur!=0 || (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0 );
+      if( !HasRowid(pTab) && IsPrimaryKeyIndex(pIx)
+       && (wctrlFlags & WHERE_ONETABLE_ONLY)!=0
+      ){
+        /* This is one term of an OR-optimization using the PRIMARY KEY of a
+        ** WITHOUT ROWID table.  No need for a separate index */
+        iIndexCur = pLevel->iTabCur;
+        op = 0;
+      }else if( pWInfo->okOnePass ){
+        Index *pJ = pTabItem->pTab->pIndex;
+        iIndexCur = iIdxCur;
+        assert( wctrlFlags & WHERE_ONEPASS_DESIRED );
+        while( ALWAYS(pJ) && pJ!=pIx ){
+          iIndexCur++;
+          pJ = pJ->pNext;
+        }
+        op = OP_OpenWrite;
+        pWInfo->aiCurOnePass[1] = iIndexCur;
+      }else if( iIdxCur && (wctrlFlags & WHERE_ONETABLE_ONLY)!=0 ){
+        iIndexCur = iIdxCur;
+        if( wctrlFlags & WHERE_REOPEN_IDX ) op = OP_ReopenIdx;
+      }else{
+        iIndexCur = pParse->nTab++;
+      }
+      pLevel->iIdxCur = iIndexCur;
+      assert( pIx->pSchema==pTab->pSchema );
+      assert( iIndexCur>=0 );
+      if( op ){
+        sqlite3VdbeAddOp3(v, op, iIndexCur, pIx->tnum, iDb);
+        sqlite3VdbeSetP4KeyInfo(pParse, pIx);
+        VdbeComment((v, "%s", pIx->zName));
+      }
+    }
+    if( iDb>=0 ) sqlite3CodeVerifySchema(pParse, iDb);
+    notReady &= ~getMask(&pWInfo->sMaskSet, pTabItem->iCursor);
+  }
+  pWInfo->iTop = sqlite3VdbeCurrentAddr(v);
+  if( db->mallocFailed ) goto whereBeginError;
+
+  /* Generate the code to do the search.  Each iteration of the for
+  ** loop below generates code for a single nested loop of the VM
+  ** program.
+  */
+  notReady = ~(Bitmask)0;
+  for(ii=0; ii<nTabList; ii++){
+    pLevel = &pWInfo->a[ii];
+#ifndef SQLITE_OMIT_AUTOMATIC_INDEX
+    if( (pLevel->pWLoop->wsFlags & WHERE_AUTO_INDEX)!=0 ){
+      constructAutomaticIndex(pParse, &pWInfo->sWC,
+                &pTabList->a[pLevel->iFrom], notReady, pLevel);
+      if( db->mallocFailed ) goto whereBeginError;
+    }
+#endif
+    explainOneScan(pParse, pTabList, pLevel, ii, pLevel->iFrom, wctrlFlags);
+    pLevel->addrBody = sqlite3VdbeCurrentAddr(v);
+    notReady = codeOneLoopStart(pWInfo, ii, notReady);
+    pWInfo->iContinue = pLevel->addrCont;
+  }
+
+  /* Done. */
+  VdbeModuleComment((v, "Begin WHERE-core"));
+  return pWInfo;
+
+  /* Jump here if malloc fails */
+whereBeginError:
+  if( pWInfo ){
+    pParse->nQueryLoop = pWInfo->savedNQueryLoop;
+    whereInfoFree(db, pWInfo);
+  }
+  return 0;
+}
+
+/*
+** Generate the end of the WHERE loop.  See comments on 
+** sqlite3WhereBegin() for additional information.
+*/
+void sqlite3WhereEnd(WhereInfo *pWInfo){
+  Parse *pParse = pWInfo->pParse;
+  Vdbe *v = pParse->pVdbe;
+  int i;
+  WhereLevel *pLevel;
+  WhereLoop *pLoop;
+  SrcList *pTabList = pWInfo->pTabList;
+  sqlite3 *db = pParse->db;
+
+  /* Generate loop termination code.
+  */
+  VdbeModuleComment((v, "End WHERE-core"));
+  sqlite3ExprCacheClear(pParse);
+  for(i=pWInfo->nLevel-1; i>=0; i--){
+    int addr;
+    pLevel = &pWInfo->a[i];
+    pLoop = pLevel->pWLoop;
+    sqlite3VdbeResolveLabel(v, pLevel->addrCont);
+    if( pLevel->op!=OP_Noop ){
+      sqlite3VdbeAddOp3(v, pLevel->op, pLevel->p1, pLevel->p2, pLevel->p3);
+      sqlite3VdbeChangeP5(v, pLevel->p5);
+      VdbeCoverage(v);
+      VdbeCoverageIf(v, pLevel->op==OP_Next);
+      VdbeCoverageIf(v, pLevel->op==OP_Prev);
+      VdbeCoverageIf(v, pLevel->op==OP_VNext);
+    }
+    if( pLoop->wsFlags & WHERE_IN_ABLE && pLevel->u.in.nIn>0 ){
+      struct InLoop *pIn;
+      int j;
+      sqlite3VdbeResolveLabel(v, pLevel->addrNxt);
+      for(j=pLevel->u.in.nIn, pIn=&pLevel->u.in.aInLoop[j-1]; j>0; j--, pIn--){
+        sqlite3VdbeJumpHere(v, pIn->addrInTop+1);
+        sqlite3VdbeAddOp2(v, pIn->eEndLoopOp, pIn->iCur, pIn->addrInTop);
+        VdbeCoverage(v);
+        VdbeCoverageIf(v, pIn->eEndLoopOp==OP_PrevIfOpen);
+        VdbeCoverageIf(v, pIn->eEndLoopOp==OP_NextIfOpen);
+        sqlite3VdbeJumpHere(v, pIn->addrInTop-1);
+      }
+      sqlite3DbFree(db, pLevel->u.in.aInLoop);
+    }
+    sqlite3VdbeResolveLabel(v, pLevel->addrBrk);
+    if( pLevel->addrSkip ){
+      sqlite3VdbeAddOp2(v, OP_Goto, 0, pLevel->addrSkip);
+      VdbeComment((v, "next skip-scan on %s", pLoop->u.btree.pIndex->zName));
+      sqlite3VdbeJumpHere(v, pLevel->addrSkip);
+      sqlite3VdbeJumpHere(v, pLevel->addrSkip-2);
+    }
+    if( pLevel->iLeftJoin ){
+      addr = sqlite3VdbeAddOp1(v, OP_IfPos, pLevel->iLeftJoin); VdbeCoverage(v);
+      assert( (pLoop->wsFlags & WHERE_IDX_ONLY)==0
+           || (pLoop->wsFlags & WHERE_INDEXED)!=0 );
+      if( (pLoop->wsFlags & WHERE_IDX_ONLY)==0 ){
+        sqlite3VdbeAddOp1(v, OP_NullRow, pTabList->a[i].iCursor);
+      }
+      if( pLoop->wsFlags & WHERE_INDEXED ){
+        sqlite3VdbeAddOp1(v, OP_NullRow, pLevel->iIdxCur);
+      }
+      if( pLevel->op==OP_Return ){
+        sqlite3VdbeAddOp2(v, OP_Gosub, pLevel->p1, pLevel->addrFirst);
+      }else{
+        sqlite3VdbeAddOp2(v, OP_Goto, 0, pLevel->addrFirst);
+      }
+      sqlite3VdbeJumpHere(v, addr);
+    }
+    VdbeModuleComment((v, "End WHERE-loop%d: %s", i,
+                     pWInfo->pTabList->a[pLevel->iFrom].pTab->zName));
+  }
+
+  /* The "break" point is here, just past the end of the outer loop.
+  ** Set it.
+  */
+  sqlite3VdbeResolveLabel(v, pWInfo->iBreak);
+
+  assert( pWInfo->nLevel<=pTabList->nSrc );
+  for(i=0, pLevel=pWInfo->a; i<pWInfo->nLevel; i++, pLevel++){
+    int k, last;
+    VdbeOp *pOp;
+    Index *pIdx = 0;
+    struct SrcList_item *pTabItem = &pTabList->a[pLevel->iFrom];
+    Table *pTab = pTabItem->pTab;
+    assert( pTab!=0 );
+    pLoop = pLevel->pWLoop;
+
+    /* For a co-routine, change all OP_Column references to the table of
+    ** the co-routine into OP_SCopy of result contained in a register.
+    ** OP_Rowid becomes OP_Null.
+    */
+    if( pTabItem->viaCoroutine && !db->mallocFailed ){
+      last = sqlite3VdbeCurrentAddr(v);
+      k = pLevel->addrBody;
+      pOp = sqlite3VdbeGetOp(v, k);
+      for(; k<last; k++, pOp++){
+        if( pOp->p1!=pLevel->iTabCur ) continue;
+        if( pOp->opcode==OP_Column ){
+          pOp->opcode = OP_Copy;
+          pOp->p1 = pOp->p2 + pTabItem->regResult;
+          pOp->p2 = pOp->p3;
+          pOp->p3 = 0;
+        }else if( pOp->opcode==OP_Rowid ){
+          pOp->opcode = OP_Null;
+          pOp->p1 = 0;
+          pOp->p3 = 0;
+        }
+      }
+      continue;
+    }
+
+    /* Close all of the cursors that were opened by sqlite3WhereBegin.
+    ** Except, do not close cursors that will be reused by the OR optimization
+    ** (WHERE_OMIT_OPEN_CLOSE).  And do not close the OP_OpenWrite cursors
+    ** created for the ONEPASS optimization.
+    */
+    if( (pTab->tabFlags & TF_Ephemeral)==0
+     && pTab->pSelect==0
+     && (pWInfo->wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0
+    ){
+      int ws = pLoop->wsFlags;
+      if( !pWInfo->okOnePass && (ws & WHERE_IDX_ONLY)==0 ){
+        sqlite3VdbeAddOp1(v, OP_Close, pTabItem->iCursor);
+      }
+      if( (ws & WHERE_INDEXED)!=0
+       && (ws & (WHERE_IPK|WHERE_AUTO_INDEX))==0 
+       && pLevel->iIdxCur!=pWInfo->aiCurOnePass[1]
+      ){
+        sqlite3VdbeAddOp1(v, OP_Close, pLevel->iIdxCur);
+      }
+    }
+
+    /* If this scan uses an index, make VDBE code substitutions to read data
+    ** from the index instead of from the table where possible.  In some cases
+    ** this optimization prevents the table from ever being read, which can
+    ** yield a significant performance boost.
+    ** 
+    ** Calls to the code generator in between sqlite3WhereBegin and
+    ** sqlite3WhereEnd will have created code that references the table
+    ** directly.  This loop scans all that code looking for opcodes
+    ** that reference the table and converts them into opcodes that
+    ** reference the index.
+    */
+    if( pLoop->wsFlags & (WHERE_INDEXED|WHERE_IDX_ONLY) ){
+      pIdx = pLoop->u.btree.pIndex;
+    }else if( pLoop->wsFlags & WHERE_MULTI_OR ){
+      pIdx = pLevel->u.pCovidx;
+    }
+    if( pIdx && !db->mallocFailed ){
+      last = sqlite3VdbeCurrentAddr(v);
+      k = pLevel->addrBody;
+      pOp = sqlite3VdbeGetOp(v, k);
+      for(; k<last; k++, pOp++){
+        if( pOp->p1!=pLevel->iTabCur ) continue;
+        if( pOp->opcode==OP_Column ){
+          int x = pOp->p2;
+          assert( pIdx->pTable==pTab );
+          if( !HasRowid(pTab) ){
+            Index *pPk = sqlite3PrimaryKeyIndex(pTab);
+            x = pPk->aiColumn[x];
+          }
+          x = sqlite3ColumnOfIndex(pIdx, x);
+          if( x>=0 ){
+            pOp->p2 = x;
+            pOp->p1 = pLevel->iIdxCur;
+          }
+          assert( (pLoop->wsFlags & WHERE_IDX_ONLY)==0 || x>=0 );
+        }else if( pOp->opcode==OP_Rowid ){
+          pOp->p1 = pLevel->iIdxCur;
+          pOp->opcode = OP_IdxRowid;
+        }
+      }
+    }
+  }
+
+  /* Final cleanup
+  */
+  pParse->nQueryLoop = pWInfo->savedNQueryLoop;
+  whereInfoFree(db, pWInfo);
+  return;
+}