remove lib/libsqlite3, it has moved back to ports

1 files changed, 0 insertions, 4608 deletions

diff --git a/lib/libsqlite3/src/where.c b/lib/libsqlite3/src/where.c
deleted file mode 100644
index 0adc698401c..00000000000
--- a/lib/libsqlite3/src/where.c
+++ /dev/null
@@ -1,4608 +0,0 @@
-/*
-** 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"
-
-/* Forward declaration of methods */
-static int whereLoopResize(sqlite3*, WhereLoop*, int);
-
-/* Test variable that can be set to enable WHERE tracing */
-#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
-/***/ int sqlite3WhereTrace = 0;
-#endif
-
-
-/*
-** 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 ONEPASS_OFF (0) if an UPDATE or DELETE statement is unable to
-** operate directly on the rowis returned by a WHERE clause.  Return
-** ONEPASS_SINGLE (1) if the statement can operation directly because only
-** a single row is to be changed.  Return ONEPASS_MULTI (2) if the one-pass
-** optimization can be used on multiple 
-**
-** 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);
-#ifdef WHERETRACE_ENABLED
-  if( sqlite3WhereTrace && pWInfo->eOnePass!=ONEPASS_OFF ){
-    sqlite3DebugPrintf("%s cursors: %d %d\n",
-         pWInfo->eOnePass==ONEPASS_SINGLE ? "ONEPASS_SINGLE" : "ONEPASS_MULTI",
-         aiCur[0], aiCur[1]);
-  }
-#endif
-  return pWInfo->eOnePass;
-}
-
-/*
-** 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;
-}
-
-/*
-** Return the bitmask for the given cursor number.  Return 0 if
-** iCursor is not in the set.
-*/
-Bitmask sqlite3WhereGetMask(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;
-}
-
-/*
-** 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 */
-  i16 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->aiCur[pScan->iEquiv-1];
-    iColumn = pScan->aiColumn[pScan->iEquiv-1];
-    if( iColumn==XN_EXPR && pScan->pIdxExpr==0 ) return 0;
-    while( (pWC = pScan->pWC)!=0 ){
-      for(pTerm=pWC->a+k; k<pWC->nTerm; k++, pTerm++){
-        if( pTerm->leftCursor==iCur
-         && pTerm->u.leftColumn==iColumn
-         && (iColumn!=XN_EXPR
-             || sqlite3ExprCompare(pTerm->pExpr->pLeft,pScan->pIdxExpr,iCur)==0)
-         && (pScan->iEquiv<=1 || !ExprHasProperty(pTerm->pExpr, EP_FromJoin))
-        ){
-          if( (pTerm->eOperator & WO_EQUIV)!=0
-           && pScan->nEquiv<ArraySize(pScan->aiCur)
-           && (pX = sqlite3ExprSkipCollate(pTerm->pExpr->pRight))->op==TK_COLUMN
-          ){
-            int j;
-            for(j=0; j<pScan->nEquiv; j++){
-              if( pScan->aiCur[j]==pX->iTable
-               && pScan->aiColumn[j]==pX->iColumn ){
-                  break;
-              }
-            }
-            if( j==pScan->nEquiv ){
-              pScan->aiCur[j] = pX->iTable;
-              pScan->aiColumn[j] = pX->iColumn;
-              pScan->nEquiv++;
-            }
-          }
-          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|WO_IS))!=0
-             && (pX = pTerm->pExpr->pRight)->op==TK_COLUMN
-             && pX->iTable==pScan->aiCur[0]
-             && pX->iColumn==pScan->aiColumn[0]
-            ){
-              testcase( pTerm->eOperator & WO_IS );
-              continue;
-            }
-            pScan->k = k+1;
-            return pTerm;
-          }
-        }
-      }
-      pScan->pWC = pScan->pWC->pOuter;
-      k = 0;
-    }
-    pScan->pWC = pScan->pOrigWC;
-    k = 0;
-    pScan->iEquiv++;
-  }
-  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 = 0;
-
-  /* memset(pScan, 0, sizeof(*pScan)); */
-  pScan->pOrigWC = pWC;
-  pScan->pWC = pWC;
-  pScan->pIdxExpr = 0;
-  if( pIdx ){
-    j = iColumn;
-    iColumn = pIdx->aiColumn[j];
-    if( iColumn==XN_EXPR ) pScan->pIdxExpr = pIdx->aColExpr->a[j].pExpr;
-  }
-  if( pIdx && iColumn>=0 ){
-    pScan->idxaff = pIdx->pTable->aCol[iColumn].affinity;
-    pScan->zCollName = pIdx->azColl[j];
-  }else{
-    pScan->idxaff = 0;
-    pScan->zCollName = 0;
-  }
-  pScan->opMask = opMask;
-  pScan->k = 0;
-  pScan->aiCur[0] = iCur;
-  pScan->aiColumn[0] = iColumn;
-  pScan->nEquiv = 1;
-  pScan->iEquiv = 1;
-  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.
-**
-** If pIdx!=0 then search for terms matching the iColumn-th column of pIdx
-** rather than the iColumn-th column of table iCur.
-**
-** 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
-** aiCur[]/iaColumn[] arrays hold X and all its equivalents. There are 11
-** slots in aiCur[]/aiColumn[] 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.
-*/
-WhereTerm *sqlite3WhereFindTerm(
-  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);
-  op &= WO_EQ|WO_IS;
-  while( p ){
-    if( (p->prereqRight & notReady)==0 ){
-      if( p->prereqRight==0 && (p->eOperator&op)!=0 ){
-        testcase( p->eOperator & WO_IS );
-        return p;
-      }
-      if( pResult==0 ) pResult = p;
-    }
-    p = whereScanNext(&scan);
-  }
-  return pResult;
-}
-
-/*
-** 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( pColl && 0==sqlite3StrICmp(pColl->zName, zColl) ){
-        return i;
-      }
-    }
-  }
-
-  return -1;
-}
-
-/*
-** Return TRUE if the iCol-th column of index pIdx is NOT NULL
-*/
-static int indexColumnNotNull(Index *pIdx, int iCol){
-  int j;
-  assert( pIdx!=0 );
-  assert( iCol>=0 && iCol<pIdx->nColumn );
-  j = pIdx->aiColumn[iCol];
-  if( j>=0 ){
-    return pIdx->pTable->aCol[j].notNull;
-  }else if( j==(-1) ){
-    return 1;
-  }else{
-    assert( j==(-2) );
-    return 0;  /* Assume an indexed expression can always yield a NULL */
-
-  }
-}
-
-/*
-** Return true if the DISTINCT expression-list passed as the third argument
-** is redundant.
-**
-** A DISTINCT list is redundant if any subset of the columns in the
-** DISTINCT list are collectively unique and individually 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++){
-      if( 0==sqlite3WhereFindTerm(pWC, iBase, i, ~(Bitmask)0, WO_EQ, pIdx) ){
-        if( findIndexCol(pParse, pDistinct, iBase, pIdx, i)<0 ) break;
-        if( indexColumnNotNull(pIdx, i)==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;
-}
-
-/*
-** Convert OP_Column opcodes to OP_Copy in previously generated code.
-**
-** This routine runs over generated VDBE code and translates OP_Column
-** opcodes into OP_Copy when the table is being accessed via co-routine 
-** instead of via table lookup.
-**
-** If the bIncrRowid parameter is 0, then any OP_Rowid instructions on
-** cursor iTabCur are transformed into OP_Null. Or, if bIncrRowid is non-zero,
-** then each OP_Rowid is transformed into an instruction to increment the
-** value stored in its output register.
-*/
-static void translateColumnToCopy(
-  Vdbe *v,            /* The VDBE containing code to translate */
-  int iStart,         /* Translate from this opcode to the end */
-  int iTabCur,        /* OP_Column/OP_Rowid references to this table */
-  int iRegister,      /* The first column is in this register */
-  int bIncrRowid      /* If non-zero, transform OP_rowid to OP_AddImm(1) */
-){
-  VdbeOp *pOp = sqlite3VdbeGetOp(v, iStart);
-  int iEnd = sqlite3VdbeCurrentAddr(v);
-  for(; iStart<iEnd; iStart++, pOp++){
-    if( pOp->p1!=iTabCur ) continue;
-    if( pOp->opcode==OP_Column ){
-      pOp->opcode = OP_Copy;
-      pOp->p1 = pOp->p2 + iRegister;
-      pOp->p2 = pOp->p3;
-      pOp->p3 = 0;
-    }else if( pOp->opcode==OP_Rowid ){
-      if( bIncrRowid ){
-        /* Increment the value stored in the P2 operand of the OP_Rowid. */
-        pOp->opcode = OP_AddImm;
-        pOp->p1 = pOp->p2;
-        pOp->p2 = 1;
-      }else{
-        pOp->opcode = OP_Null;
-        pOp->p1 = 0;
-        pOp->p3 = 0;
-      }
-    }
-  }
-}
-
-/*
-** 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|WO_IS))==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;
-  testcase( pTerm->pExpr->op==TK_IS );
-  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 */
-  Expr *pPartial = 0;         /* Partial Index Expression */
-  int iContinue = 0;          /* Jump here to skip excluded rows */
-  struct SrcList_item *pTabItem;  /* FROM clause term being indexed */
-  int addrCounter;            /* Address where integer counter is initialized */
-  int regBase;                /* Array of registers where record is assembled */
-
-  /* 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++){
-    Expr *pExpr = pTerm->pExpr;
-    assert( !ExprHasProperty(pExpr, EP_FromJoin)    /* prereq always non-zero */
-         || pExpr->iRightJoinTable!=pSrc->iCursor   /*   for the right-hand   */
-         || pLoop->prereq!=0 );                     /*   table of a LEFT JOIN */
-    if( pLoop->prereq==0
-     && (pTerm->wtFlags & TERM_VIRTUAL)==0
-     && !ExprHasProperty(pExpr, EP_FromJoin)
-     && sqlite3ExprIsTableConstant(pExpr, pSrc->iCursor) ){
-      pPartial = sqlite3ExprAnd(pParse->db, pPartial,
-                                sqlite3ExprDup(pParse->db, pExpr, 0));
-    }
-    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) ){
-          goto end_auto_index_create;
-        }
-        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 = MIN(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;
-  }
-
-  /* Construct the Index object to describe this index */
-  pIdx = sqlite3AllocateIndexObject(pParse->db, nKeyCol+1, 0, &zNotUsed);
-  if( pIdx==0 ) goto end_auto_index_create;
-  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] = 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] = XN_ROWID;
-  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 */
-  sqlite3ExprCachePush(pParse);
-  pTabItem = &pWC->pWInfo->pTabList->a[pLevel->iFrom];
-  if( pTabItem->fg.viaCoroutine ){
-    int regYield = pTabItem->regReturn;
-    addrCounter = sqlite3VdbeAddOp2(v, OP_Integer, 0, 0);
-    sqlite3VdbeAddOp3(v, OP_InitCoroutine, regYield, 0, pTabItem->addrFillSub);
-    addrTop =  sqlite3VdbeAddOp1(v, OP_Yield, regYield);
-    VdbeCoverage(v);
-    VdbeComment((v, "next row of \"%s\"", pTabItem->pTab->zName));
-  }else{
-    addrTop = sqlite3VdbeAddOp1(v, OP_Rewind, pLevel->iTabCur); VdbeCoverage(v);
-  }
-  if( pPartial ){
-    iContinue = sqlite3VdbeMakeLabel(v);
-    sqlite3ExprIfFalse(pParse, pPartial, iContinue, SQLITE_JUMPIFNULL);
-    pLoop->wsFlags |= WHERE_PARTIALIDX;
-  }
-  regRecord = sqlite3GetTempReg(pParse);
-  regBase = sqlite3GenerateIndexKey(
-      pParse, pIdx, pLevel->iTabCur, regRecord, 0, 0, 0, 0
-  );
-  sqlite3VdbeAddOp2(v, OP_IdxInsert, pLevel->iIdxCur, regRecord);
-  sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);
-  if( pPartial ) sqlite3VdbeResolveLabel(v, iContinue);
-  if( pTabItem->fg.viaCoroutine ){
-    sqlite3VdbeChangeP2(v, addrCounter, regBase+n);
-    translateColumnToCopy(v, addrTop, pLevel->iTabCur, pTabItem->regResult, 1);
-    sqlite3VdbeGoto(v, addrTop);
-    pTabItem->fg.viaCoroutine = 0;
-  }else{
-    sqlite3VdbeAddOp2(v, OP_Next, pLevel->iTabCur, addrTop+1); VdbeCoverage(v);
-  }
-  sqlite3VdbeChangeP5(v, SQLITE_STMTSTATUS_AUTOINDEX);
-  sqlite3VdbeJumpHere(v, addrTop);
-  sqlite3ReleaseTempReg(pParse, regRecord);
-  sqlite3ExprCachePop(pParse);
-  
-  /* Jump here when skipping the initialization */
-  sqlite3VdbeJumpHere(v, addrInit);
-
-end_auto_index_create:
-  sqlite3ExprDelete(pParse->db, pPartial);
-}
-#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,
-  Bitmask mUnusable,              /* Ignore terms with these prereqs */
-  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;
-    if( pTerm->prereqRight & mUnusable ) continue;
-    assert( IsPowerOfTwo(pTerm->eOperator & ~WO_EQUIV) );
-    testcase( pTerm->eOperator & WO_IN );
-    testcase( pTerm->eOperator & WO_ISNULL );
-    testcase( pTerm->eOperator & WO_IS );
-    testcase( pTerm->eOperator & WO_ALL );
-    if( (pTerm->eOperator & ~(WO_ISNULL|WO_EQUIV|WO_IS))==0 ) continue;
-    if( pTerm->wtFlags & TERM_VNULL ) continue;
-    assert( pTerm->u.leftColumn>=(-1) );
-    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;
-    if( pTerm->prereqRight & mUnusable ) continue;
-    assert( IsPowerOfTwo(pTerm->eOperator & ~WO_EQUIV) );
-    testcase( pTerm->eOperator & WO_IN );
-    testcase( pTerm->eOperator & WO_IS );
-    testcase( pTerm->eOperator & WO_ISNULL );
-    testcase( pTerm->eOperator & WO_ALL );
-    if( (pTerm->eOperator & ~(WO_ISNULL|WO_EQUIV|WO_IS))==0 ) continue;
-    if( pTerm->wtFlags & TERM_VNULL ) continue;
-    assert( pTerm->u.leftColumn>=(-1) );
-    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 pRec
-**    aStat[1]      Est. number of rows equal to pRec
-**
-** Return the index of the sample that is the smallest sample that
-** is greater than or equal to pRec. Note that this index is not an index
-** into the aSample[] array - it is an index into a virtual set of samples
-** based on the contents of aSample[] and the number of fields in record 
-** pRec. 
-*/
-static int 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 i;                      /* Index of first sample >= pRec */
-  int iSample;                /* Smallest sample larger than or equal to pRec */
-  int iMin = 0;               /* Smallest sample not yet tested */
-  int iTest;                  /* Next sample to test */
-  int res;                    /* Result of comparison operation */
-  int nField;                 /* Number of fields in pRec */
-  tRowcnt iLower = 0;         /* anLt[] + anEq[] of largest sample pRec is > */
-
-#ifndef SQLITE_DEBUG
-  UNUSED_PARAMETER( pParse );
-#endif
-  assert( pRec!=0 );
-  assert( pIdx->nSample>0 );
-  assert( pRec->nField>0 && pRec->nField<=pIdx->nSampleCol );
-
-  /* Do a binary search to find the first sample greater than or equal
-  ** to pRec. If pRec contains a single field, the set of samples to search
-  ** is simply the aSample[] array. If the samples in aSample[] contain more
-  ** than one fields, all fields following the first are ignored.
-  **
-  ** If pRec contains N fields, where N is more than one, then as well as the
-  ** samples in aSample[] (truncated to N fields), the search also has to
-  ** consider prefixes of those samples. For example, if the set of samples
-  ** in aSample is:
-  **
-  **     aSample[0] = (a, 5) 
-  **     aSample[1] = (a, 10) 
-  **     aSample[2] = (b, 5) 
-  **     aSample[3] = (c, 100) 
-  **     aSample[4] = (c, 105)
-  **
-  ** Then the search space should ideally be the samples above and the 
-  ** unique prefixes [a], [b] and [c]. But since that is hard to organize, 
-  ** the code actually searches this set:
-  **
-  **     0: (a) 
-  **     1: (a, 5) 
-  **     2: (a, 10) 
-  **     3: (a, 10) 
-  **     4: (b) 
-  **     5: (b, 5) 
-  **     6: (c) 
-  **     7: (c, 100) 
-  **     8: (c, 105)
-  **     9: (c, 105)
-  **
-  ** For each sample in the aSample[] array, N samples are present in the
-  ** effective sample array. In the above, samples 0 and 1 are based on 
-  ** sample aSample[0]. Samples 2 and 3 on aSample[1] etc.
-  **
-  ** Often, sample i of each block of N effective samples has (i+1) fields.
-  ** Except, each sample may be extended to ensure that it is greater than or
-  ** equal to the previous sample in the array. For example, in the above, 
-  ** sample 2 is the first sample of a block of N samples, so at first it 
-  ** appears that it should be 1 field in size. However, that would make it 
-  ** smaller than sample 1, so the binary search would not work. As a result, 
-  ** it is extended to two fields. The duplicates that this creates do not 
-  ** cause any problems.
-  */
-  nField = pRec->nField;
-  iCol = 0;
-  iSample = pIdx->nSample * nField;
-  do{
-    int iSamp;                    /* Index in aSample[] of test sample */
-    int n;                        /* Number of fields in test sample */
-
-    iTest = (iMin+iSample)/2;
-    iSamp = iTest / nField;
-    if( iSamp>0 ){
-      /* The proposed effective sample is a prefix of sample aSample[iSamp].
-      ** Specifically, the shortest prefix of at least (1 + iTest%nField) 
-      ** fields that is greater than the previous effective sample.  */
-      for(n=(iTest % nField) + 1; n<nField; n++){
-        if( aSample[iSamp-1].anLt[n-1]!=aSample[iSamp].anLt[n-1] ) break;
-      }
-    }else{
-      n = iTest + 1;
-    }
-
-    pRec->nField = n;
-    res = sqlite3VdbeRecordCompare(aSample[iSamp].n, aSample[iSamp].p, pRec);
-    if( res<0 ){
-      iLower = aSample[iSamp].anLt[n-1] + aSample[iSamp].anEq[n-1];
-      iMin = iTest+1;
-    }else if( res==0 && n<nField ){
-      iLower = aSample[iSamp].anLt[n-1];
-      iMin = iTest+1;
-      res = -1;
-    }else{
-      iSample = iTest;
-      iCol = n-1;
-    }
-  }while( res && iMin<iSample );
-  i = iSample / nField;
-
-#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( pParse->db->mallocFailed==0 ){
-    if( res==0 ){
-      /* If (res==0) is true, then pRec must be equal to sample i. */
-      assert( i<pIdx->nSample );
-      assert( iCol==nField-1 );
-      pRec->nField = nField;
-      assert( 0==sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec) 
-           || pParse->db->mallocFailed 
-      );
-    }else{
-      /* Unless i==pIdx->nSample, indicating that pRec is larger than
-      ** all samples in the aSample[] array, pRec must be smaller than the
-      ** (iCol+1) field prefix of sample i.  */
-      assert( i<=pIdx->nSample && i>=0 );
-      pRec->nField = iCol+1;
-      assert( i==pIdx->nSample 
-           || sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec)>0
-           || pParse->db->mallocFailed );
-
-      /* if i==0 and iCol==0, then record pRec is smaller than all samples
-      ** in the aSample[] array. Otherwise, if (iCol>0) then pRec must
-      ** be greater than or equal to the (iCol) field prefix of sample i.
-      ** If (i>0), then pRec must also be greater than sample (i-1).  */
-      if( iCol>0 ){
-        pRec->nField = iCol;
-        assert( sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec)<=0
-             || pParse->db->mallocFailed );
-      }
-      if( i>0 ){
-        pRec->nField = nField;
-        assert( sqlite3VdbeRecordCompare(aSample[i-1].n, aSample[i-1].p, pRec)<0
-             || pParse->db->mallocFailed );
-      }
-    }
-  }
-#endif /* ifdef SQLITE_DEBUG */
-
-  if( res==0 ){
-    /* Record pRec is equal to sample i */
-    assert( iCol==nField-1 );
-    aStat[0] = aSample[i].anLt[iCol];
-    aStat[1] = aSample[i].anEq[iCol];
-  }else{
-    /* At this point, the (iCol+1) field prefix of aSample[i] is the first 
-    ** sample that is greater than pRec. Or, if i==pIdx->nSample then pRec
-    ** is larger than all samples in the array. */
-    tRowcnt iUpper, iGap;
-    if( i>=pIdx->nSample ){
-      iUpper = sqlite3LogEstToInt(pIdx->aiRowLogEst[0]);
-    }else{
-      iUpper = aSample[i].anLt[iCol];
-    }
-
-    if( iLower>=iUpper ){
-      iGap = 0;
-    }else{
-      iGap = iUpper - iLower;
-    }
-    if( roundUp ){
-      iGap = (iGap*2)/3;
-    }else{
-      iGap = iGap/3;
-    }
-    aStat[0] = iLower + iGap;
-    aStat[1] = pIdx->aAvgEq[iCol];
-  }
-
-  /* Restore the pRec->nField value before returning.  */
-  pRec->nField = nField;
-  return i;
-}
-#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
-/*
-** Return the affinity for a single column of an index.
-*/
-static char sqlite3IndexColumnAffinity(sqlite3 *db, Index *pIdx, int iCol){
-  assert( iCol>=0 && iCol<pIdx->nColumn );
-  if( !pIdx->zColAff ){
-    if( sqlite3IndexAffinityStr(db, pIdx)==0 ) return SQLITE_AFF_BLOB;
-  }
-  return pIdx->zColAff[iCol];
-}
-#endif
-
-
-#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;
-  u8 aff = sqlite3IndexColumnAffinity(db, p, nEq);
-  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 number 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, then *pnOut 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 ){
-    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 is 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 $U is available, both values
-      ** of iUpper are requested of whereKeyStats() and the smaller used.
-      **
-      ** The number of rows between the two bounds is then just iUpper-iLower.
-      */
-      tRowcnt iLower;     /* Rows less than the lower bound */
-      tRowcnt iUpper;     /* Rows less than the upper bound */
-      int iLwrIdx = -2;   /* aSample[] for the lower bound */
-      int iUprIdx = -1;   /* aSample[] for the upper bound */
-
-      if( pRec ){
-        testcase( pRec->nField!=pBuilder->nRecValid );
-        pRec->nField = pBuilder->nRecValid;
-      }
-      aff = sqlite3IndexColumnAffinity(pParse->db, p, nEq);
-      assert( nEq!=p->nKeyCol || aff==SQLITE_AFF_INTEGER );
-      /* Determine iLower and iUpper using ($P) only. */
-      if( nEq==0 ){
-        iLower = 0;
-        iUpper = p->nRowEst0;
-      }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:$L). */
-      if( pLower ){
-        int bOk;                    /* True if value is extracted from pExpr */
-        Expr *pExpr = pLower->pExpr->pRight;
-        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
-        if( rc==SQLITE_OK && bOk ){
-          tRowcnt iNew;
-          iLwrIdx = whereKeyStats(pParse, p, pRec, 0, a);
-          iNew = a[0] + ((pLower->eOperator & (WO_GT|WO_LE)) ? a[1] : 0);
-          if( iNew>iLower ) iLower = iNew;
-          nOut--;
-          pLower = 0;
-        }
-      }
-
-      /* If possible, improve on the iUpper estimate using ($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;
-          iUprIdx = 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);
-          /* TUNING:  If both iUpper and iLower are derived from the same
-          ** sample, then assume they are 4x more selective.  This brings
-          ** the estimated selectivity more in line with what it would be
-          ** if estimated without the use of STAT3/4 tables. */
-          if( iLwrIdx==iUprIdx ) nNew -= 20;  assert( 20==sqlite3LogEst(4) );
-        }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 and neither limit
-  ** has an application-defined likelihood(), 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 && pLower->truthProb>0 && pUpper && pUpper->truthProb>0 ){
-    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 = sqlite3IndexColumnAffinity(pParse->db, p, nEq-1);
-  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 */
-
-
-#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 wtFlags=0x%04x\n",
-       iTerm, pTerm, zType, pTerm->leftCursor, pTerm->truthProb,
-       pTerm->eOperator, pTerm->wtFlags);
-    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->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);
-      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) ){
-    int i;
-    for(i=0; i<pWInfo->nLevel; i++){
-      WhereLevel *pLevel = &pWInfo->a[i];
-      if( pLevel->pWLoop && (pLevel->pWLoop->wsFlags & WHERE_IN_ABLE) ){
-        sqlite3DbFree(db, pLevel->u.in.aInLoop);
-      }
-    }
-    sqlite3WhereClauseClear(&pWInfo->sWC);
-    while( pWInfo->pLoops ){
-      WhereLoop *p = pWInfo->pLoops;
-      pWInfo->pLoops = p->pNextLoop;
-      whereLoopDelete(db, p);
-    }
-    sqlite3DbFree(db, pWInfo);
-  }
-}
-
-/*
-** Return TRUE if all of the following are true:
-**
-**   (1)  X has the same or lower cost that Y
-**   (2)  X is a proper subset of Y
-**   (3)  X skips at least as many columns as 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.  The third rule
-** was added because if X uses skip-scan less than Y it still might
-** deserve a lower cost even if it is a proper subset of Y.
-*/
-static int whereLoopCheaperProperSubset(
-  const WhereLoop *pX,       /* First WhereLoop to compare */
-  const WhereLoop *pY        /* Compare against this WhereLoop */
-){
-  int i, j;
-  if( pX->nLTerm-pX->nSkip >= pY->nLTerm-pY->nSkip ){
-    return 0; /* X is not a subset of Y */
-  }
-  if( pY->nSkip > pX->nSkip ) return 0;
-  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--){
-    if( pX->aLTerm[i]==0 ) continue;
-    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.
-*/
-static void whereLoopAdjustCost(const WhereLoop *p, WhereLoop *pTemplate){
-  if( (pTemplate->wsFlags & WHERE_INDEXED)==0 ) return;
-  for(; p; p=p->pNextLoop){
-    if( p->iTab!=pTemplate->iTab ) continue;
-    if( (p->wsFlags & WHERE_INDEXED)==0 ) continue;
-    if( whereLoopCheaperProperSubset(p, pTemplate) ){
-      /* Adjust pTemplate cost downward so that it is cheaper than its 
-      ** subset p. */
-      WHERETRACE(0x80,("subset cost adjustment %d,%d to %d,%d\n",
-                       pTemplate->rRun, pTemplate->nOut, p->rRun, p->nOut-1));
-      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 */
-      WHERETRACE(0x80,("subset cost adjustment %d,%d to %d,%d\n",
-                       pTemplate->rRun, pTemplate->nOut, p->rRun, p->nOut+1));
-      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. Unless it is a skip-scan. */
-    if( (p->wsFlags & WHERE_AUTO_INDEX)!=0
-     && (pTemplate->nSkip)==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( pTemplate->nLTerm ){
-#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.
-*
-** For every WHERE clause term that is not used by the index
-** and which has a truth probability assigned by one of the likelihood(),
-** likely(), or unlikely() SQL functions, reduce the estimated number
-** of output rows by the probability specified.
-**
-** TUNING:  For every WHERE clause term that is not used by the index
-** and which does not have an assigned truth probability, heuristics
-** described below are used to try to estimate the truth probability.
-** TODO --> Perhaps this is something that could be improved by better
-** table statistics.
-**
-** Heuristic 1:  Estimate the truth probability as 93.75%.  The 93.75%
-** value corresponds to -1 in LogEst notation, so this means decrement
-** the WhereLoop.nOut field for every such WHERE clause term.
-**
-** Heuristic 2:  If there exists one or more WHERE clause terms of the
-** form "x==EXPR" and EXPR is not a constant 0 or 1, then make sure the
-** final output row estimate is no greater than 1/4 of the total number
-** of rows in the table.  In other words, assume that x==EXPR will filter
-** out at least 3 out of 4 rows.  If EXPR is -1 or 0 or 1, then maybe the
-** "x" column is boolean or else -1 or 0 or 1 is a common default value
-** on the "x" column and so in that case only cap the output row estimate
-** at 1/2 instead of 1/4.
-*/
-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, k;
-  LogEst iReduce = 0;    /* pLoop->nOut should not exceed nRow-iReduce */
-
-  assert( (pLoop->wsFlags & WHERE_AUTO_INDEX)==0 );
-  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 ){
-        /* If a truth probability is specified using the likelihood() hints,
-        ** then use the probability provided by the application. */
-        pLoop->nOut += pTerm->truthProb;
-      }else{
-        /* In the absence of explicit truth probabilities, use heuristics to
-        ** guess a reasonable truth probability. */
-        pLoop->nOut--;
-        if( pTerm->eOperator&(WO_EQ|WO_IS) ){
-          Expr *pRight = pTerm->pExpr->pRight;
-          testcase( pTerm->pExpr->op==TK_IS );
-          if( sqlite3ExprIsInteger(pRight, &k) && k>=(-1) && k<=1 ){
-            k = 10;
-          }else{
-            k = 20;
-          }
-          if( iReduce<k ) iReduce = k;
-        }
-      }
-    }
-  }
-  if( pLoop->nOut > nRow-iReduce )  pLoop->nOut = nRow - iReduce;
-}
-
-/*
-** 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->nSkip */
-  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */
-  LogEst saved_nOut;              /* Original value of pNew->nOut */
-  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->fg.jointype & JT_LEFT)!=0 ){
-    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE;
-  }else{
-    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE|WO_ISNULL|WO_IS;
-  }
-  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);
-
-  assert( pNew->u.btree.nEq<pProbe->nColumn );
-
-  saved_nEq = pNew->u.btree.nEq;
-  saved_nSkip = pNew->nSkip;
-  saved_nLTerm = pNew->nLTerm;
-  saved_wsFlags = pNew->wsFlags;
-  saved_prereq = pNew->prereq;
-  saved_nOut = pNew->nOut;
-  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, saved_nEq,
-                        opMask, pProbe);
-  pNew->rSetup = 0;
-  rSize = pProbe->aiRowLogEst[0];
-  rLogSize = estLog(rSize);
-  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)
-     && indexColumnNotNull(pProbe, saved_nEq)
-    ){
-      continue; /* ignore IS [NOT] NULL constraints on NOT NULL columns */
-    }
-    if( pTerm->prereqRight & pNew->maskSelf ) continue;
-
-    /* Do not allow the upper bound of a LIKE optimization range constraint
-    ** to mix with a lower range bound from some other source */
-    if( pTerm->wtFlags & TERM_LIKEOPT && pTerm->eOperator==WO_LT ) 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|WO_IS) ){
-      int iCol = pProbe->aiColumn[saved_nEq];
-      pNew->wsFlags |= WHERE_COLUMN_EQ;
-      assert( saved_nEq==pNew->u.btree.nEq );
-      if( iCol==XN_ROWID 
-       || (iCol>0 && nInMul==0 && saved_nEq==pProbe->nKeyCol-1)
-      ){
-        if( iCol>=0 && pProbe->uniqNotNull==0 ){
-          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;
-      if( pTerm->wtFlags & TERM_LIKEOPT ){
-        /* Range contraints that come from the LIKE optimization are
-        ** always used in pairs. */
-        pTop = &pTerm[1];
-        assert( (pTop-(pTerm->pWC->a))<pTerm->pWC->nTerm );
-        assert( pTop->wtFlags & TERM_LIKEOPT );
-        assert( pTop->eOperator==WO_LT );
-        if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
-        pNew->aLTerm[pNew->nLTerm++] = pTop;
-        pNew->wsFlags |= WHERE_TOP_LIMIT;
-      }
-    }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|WO_IS) );
-
-      assert( pNew->nOut==saved_nOut );
-      if( pTerm->truthProb<=0 && pProbe->aiColumn[saved_nEq]>=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
-         && ((eOp & WO_IN)==0 || !ExprHasProperty(pTerm->pExpr, EP_xIsSelect))
-        ){
-          Expr *pExpr = pTerm->pExpr;
-          if( (eOp & (WO_EQ|WO_ISNULL|WO_IS))!=0 ){
-            testcase( eOp & WO_EQ );
-            testcase( eOp & WO_IS );
-            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->nSkip = saved_nSkip;
-  pNew->wsFlags = saved_wsFlags;
-  pNew->nOut = saved_nOut;
-  pNew->nLTerm = saved_nLTerm;
-
-  /* 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->noSkipScan==0
-   && 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->nSkip++;
-    pNew->aLTerm[pNew->nLTerm++] = 0;
-    pNew->wsFlags |= WHERE_SKIPSCAN;
-    nIter = pProbe->aiRowLogEst[saved_nEq] - pProbe->aiRowLogEst[saved_nEq+1];
-    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->nSkip = saved_nSkip;
-    pNew->wsFlags = saved_wsFlags;
-  }
-
-  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;
-  ExprList *aColExpr;
-  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 && pExpr->iTable==iCursor ){
-      if( pExpr->iColumn<0 ) return 1;
-      for(jj=0; jj<pIndex->nKeyCol; jj++){
-        if( pExpr->iColumn==pIndex->aiColumn[jj] ) return 1;
-      }
-    }else if( (aColExpr = pIndex->aColExpr)!=0 ){
-      for(jj=0; jj<pIndex->nKeyCol; jj++){
-        if( pIndex->aiColumn[jj]!=XN_EXPR ) continue;
-        if( sqlite3ExprCompare(pExpr,aColExpr->a[jj].pExpr,iCursor)==0 ){
-          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;
-  while( pWhere->op==TK_AND ){
-    if( !whereUsablePartialIndex(iTab,pWC,pWhere->pLeft) ) return 0;
-    pWhere = pWhere->pRight;
-  }
-  for(i=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
-    Expr *pExpr = pTerm->pExpr;
-    if( sqlite3ExprImpliesExpr(pExpr, pWhere, iTab) 
-     && (!ExprHasProperty(pExpr, EP_FromJoin) || pExpr->iRightJoinTable==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->pIBIndex ){
-    /* An INDEXED BY clause specifies a particular index to use */
-    pProbe = pSrc->pIBIndex;
-  }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->fg.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      /* Not part of an OR optimization */
-   && (pWInfo->wctrlFlags & WHERE_NO_AUTOINDEX)==0
-   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0
-   && pSrc->pIBIndex==0      /* Has no INDEXED BY clause */
-   && !pSrc->fg.notIndexed   /* Has no NOT INDEXED clause */
-   && HasRowid(pTab)         /* Not WITHOUT ROWID table. (FIXME: Why not?) */
-   && !pSrc->fg.isCorrelated /* Not a correlated subquery */
-   && !pSrc->fg.isRecursive  /* Not a recursive common table expression. */
-  ){
-    /* 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->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->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->pIBIndex ) 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.
-**
-** If there are no LEFT or CROSS JOIN joins in the query, both mExtra and
-** mUnusable are set to 0. Otherwise, mExtra is a mask of all FROM clause
-** entries that occur before the virtual table in the FROM clause and are
-** separated from it by at least one LEFT or CROSS JOIN. Similarly, the
-** mUnusable mask contains all FROM clause entries that occur after the
-** virtual table and are separated from it by at least one LEFT or 
-** CROSS JOIN. 
-**
-** For example, if the query were:
-**
-**   ... FROM t1, t2 LEFT JOIN t3, t4, vt CROSS JOIN t5, t6;
-**
-** then mExtra corresponds to (t1, t2) and mUnusable to (t5, t6).
-**
-** All the tables in mExtra must be scanned before the current virtual 
-** table. So any terms for which all prerequisites are satisfied by 
-** mExtra may be specified as "usable" in all calls to xBestIndex. 
-** Conversely, all tables in mUnusable must be scanned after the current
-** virtual table, so any terms for which the prerequisites overlap with
-** mUnusable should always be configured as "not-usable" for xBestIndex.
-*/
-static int whereLoopAddVirtual(
-  WhereLoopBuilder *pBuilder,  /* WHERE clause information */
-  Bitmask mExtra,              /* Tables that must be scanned before this one */
-  Bitmask mUnusable            /* Tables that must be scanned after this one */
-){
-  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;
-
-  assert( (mExtra & mUnusable)==0 );
-  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, mUnusable, 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 & ~mExtra)!=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 & ~mExtra)==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;
-    pIdxInfo->idxFlags = 0;
-    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;
-          pIdxInfo->idxFlags &= ~SQLITE_INDEX_SCAN_UNIQUE;
-        }
-      }
-    }
-    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);
-
-      /* Set the WHERE_ONEROW flag if the xBestIndex() method indicated
-      ** that the scan will visit at most one row. Clear it otherwise. */
-      if( pIdxInfo->idxFlags & SQLITE_INDEX_SCAN_UNIQUE ){
-        pNew->wsFlags |= WHERE_ONEROW;
-      }else{
-        pNew->wsFlags &= ~WHERE_ONEROW;
-      }
-      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, 
-  Bitmask mUnusable
-){
-  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, mUnusable);
-        }else
-#endif
-        {
-          rc = whereLoopAddBtree(&sSubBuild, mExtra);
-        }
-        if( rc==SQLITE_OK ){
-          rc = whereLoopAddOr(&sSubBuild, mExtra, mUnusable);
-        }
-        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;
-  struct SrcList_item *pEnd = &pTabList->a[pWInfo->nLevel];
-  sqlite3 *db = pWInfo->pParse->db;
-  int rc = SQLITE_OK;
-  WhereLoop *pNew;
-  u8 priorJointype = 0;
-
-  /* Loop over the tables in the join, from left to right */
-  pNew = pBuilder->pNew;
-  whereLoopInit(pNew);
-  for(iTab=0, pItem=pTabList->a; pItem<pEnd; iTab++, pItem++){
-    Bitmask mUnusable = 0;
-    pNew->iTab = iTab;
-    pNew->maskSelf = sqlite3WhereGetMask(&pWInfo->sMaskSet, pItem->iCursor);
-    if( ((pItem->fg.jointype|priorJointype) & (JT_LEFT|JT_CROSS))!=0 ){
-      /* This condition is true when pItem is the FROM clause term on the
-      ** right-hand-side of a LEFT or CROSS JOIN.  */
-      mExtra = mPrior;
-    }
-    priorJointype = pItem->fg.jointype;
-    if( IsVirtual(pItem->pTab) ){
-      struct SrcList_item *p;
-      for(p=&pItem[1]; p<pEnd; p++){
-        if( mUnusable || (p->fg.jointype & (JT_LEFT|JT_CROSS)) ){
-          mUnusable |= sqlite3WhereGetMask(&pWInfo->sMaskSet, p->iCursor);
-        }
-      }
-      rc = whereLoopAddVirtual(pBuilder, mExtra, mUnusable);
-    }else{
-      rc = whereLoopAddBtree(pBuilder, mExtra);
-    }
-    if( rc==SQLITE_OK ){
-      rc = whereLoopAddOr(pBuilder, mExtra, mUnusable);
-    }
-    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 = sqlite3WhereFindTerm(&pWInfo->sWC, iCur, pOBExpr->iColumn,
-                       ~ready, WO_EQ|WO_ISNULL|WO_IS, 0);
-      if( pTerm==0 ) continue;
-      if( (pTerm->eOperator&(WO_EQ|WO_IS))!=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;
-        testcase( pTerm->pExpr->op==TK_IS );
-      }
-      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]==XN_ROWID
-                          || !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->nSkip==0
-         && ((i = pLoop->aLTerm[j]->eOperator) & (WO_EQ|WO_ISNULL|WO_IS))!=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 = XN_ROWID;
-          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( iColumn>=(-1) ){
-            if( pOBExpr->op!=TK_COLUMN ) continue;
-            if( pOBExpr->iTable!=iCur ) continue;
-            if( pOBExpr->iColumn!=iColumn ) continue;
-          }else{
-            if( sqlite3ExprCompare(pOBExpr,pIndex->aColExpr->a[j].pExpr,iCur) ){
-              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 = sqlite3WhereExprUsage(&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 28.  If the cost
-  ** of computing an automatic index is not paid back within the first 28
-  ** rows, then do not use the automatic index. */
-  aFrom[0].nRow = MIN(pParse->nQueryLoop, 48);  assert( 48==sqlite3LogEst(28) );
-  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 & 0x02 ){
-      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 && nLoop>0
-    ){
-      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->fg.isIndexedBy ) return 0;
-  iCur = pItem->iCursor;
-  pWC = &pWInfo->sWC;
-  pLoop = pBuilder->pNew;
-  pLoop->wsFlags = 0;
-  pLoop->nSkip = 0;
-  pTerm = sqlite3WhereFindTerm(pWC, iCur, -1, 0, WO_EQ|WO_IS, 0);
-  if( pTerm ){
-    testcase( pTerm->eOperator & WO_IS );
-    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){
-      int opMask;
-      assert( pLoop->aLTermSpace==pLoop->aLTerm );
-      if( !IsUniqueIndex(pIdx)
-       || pIdx->pPartIdxWhere!=0 
-       || pIdx->nKeyCol>ArraySize(pLoop->aLTermSpace) 
-      ) continue;
-      opMask = pIdx->uniqNotNull ? (WO_EQ|WO_IS) : WO_EQ;
-      for(j=0; j<pIdx->nKeyCol; j++){
-        pTerm = sqlite3WhereFindTerm(pWC, iCur, j, 0, opMask, pIdx);
-        if( pTerm==0 ) break;
-        testcase( pTerm->eOperator & WO_IS );
-        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 = sqlite3WhereGetMask(&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 */
-
-  assert( (wctrlFlags & WHERE_ONEPASS_MULTIROW)==0 || (
-        (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 
-     && (wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0 
-  ));
-
-  /* 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;
-  assert( pWInfo->eOnePass==ONEPASS_OFF );  /* ONEPASS defaults to OFF */
-  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);
-  sqlite3WhereClauseInit(&pWInfo->sWC, pWInfo);
-  sqlite3WhereSplit(&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.
-  **
-  ** The N-th term of the FROM clause is assigned a bitmask of 1<<N.
-  **
-  ** The rule of the previous sentence ensures thta if X is the bitmask for
-  ** a table T, then X-1 is the bitmask for all other tables to the left of T.
-  ** 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);
-    sqlite3WhereTabFuncArgs(pParse, &pTabList->a[ii], &pWInfo->sWC);
-  }
-#ifdef SQLITE_DEBUG
-  for(ii=0; ii<pTabList->nSrc; ii++){
-    Bitmask m = sqlite3WhereGetMask(pMaskSet, pTabList->a[ii].iCursor);
-    assert( m==MASKBIT(ii) );
-  }
-#endif
-
-  /* Analyze all of the subexpressions. */
-  sqlite3WhereExprAnalyze(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 *** (wctrlFlags: 0x%x)\n",
-             wctrlFlags));
-#if defined(WHERETRACE_ENABLED)
-  if( sqlite3WhereTrace & 0x100 ){ /* Display all terms of the WHERE clause */
-    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;
-  
-#ifdef WHERETRACE_ENABLED
-    if( sqlite3WhereTrace ){    /* Display all of the WhereLoop objects */
-      WhereLoop *p;
-      int i;
-      static const 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
-  if( sqlite3WhereTrace ){
-    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 = sqlite3WhereExprListUsage(pMaskSet, pResultSet);
-    if( sWLB.pOrderBy ){
-      tabUsed |= sqlite3WhereExprListUsage(pMaskSet, sWLB.pOrderBy);
-    }
-    while( pWInfo->nLevel>=2 ){
-      WhereTerm *pTerm, *pEnd;
-      pLoop = pWInfo->a[pWInfo->nLevel-1].pWLoop;
-      if( (pWInfo->pTabList->a[pLoop->iTab].fg.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 or delete a single row.
-  */
-  assert( (wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || pWInfo->nLevel==1 );
-  if( (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 ){
-    int wsFlags = pWInfo->a[0].pWLoop->wsFlags;
-    int bOnerow = (wsFlags & WHERE_ONEROW)!=0;
-    if( bOnerow || ( (wctrlFlags & WHERE_ONEPASS_MULTIROW)
-       && 0==(wsFlags & WHERE_VIRTUALTABLE)
-    )){
-      pWInfo->eOnePass = bOnerow ? ONEPASS_SINGLE : ONEPASS_MULTI;
-      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.
-  */
-  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->eOnePass!=ONEPASS_OFF ){
-        op = OP_OpenWrite;
-        pWInfo->aiCurOnePass[0] = pTabItem->iCursor;
-      };
-      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);
-      assert( pTabItem->iCursor==pLevel->iTabCur );
-      testcase( pWInfo->eOnePass==ONEPASS_OFF && pTab->nCol==BMS-1 );
-      testcase( pWInfo->eOnePass==ONEPASS_OFF && pTab->nCol==BMS );
-      if( pWInfo->eOnePass==ONEPASS_OFF && 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 );
-      }
-#ifdef SQLITE_ENABLE_COLUMN_USED_MASK
-      sqlite3VdbeAddOp4Dup8(v, OP_ColumnsUsed, pTabItem->iCursor, 0, 0,
-                            (const u8*)&pTabItem->colUsed, P4_INT64);
-#endif
-    }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->eOnePass!=ONEPASS_OFF ){
-        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);
-        if( (pLoop->wsFlags & WHERE_CONSTRAINT)!=0
-         && (pLoop->wsFlags & (WHERE_COLUMN_RANGE|WHERE_SKIPSCAN))==0
-         && (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)==0
-        ){
-          sqlite3VdbeChangeP5(v, OPFLAG_SEEKEQ); /* Hint to COMDB2 */
-        }
-        VdbeComment((v, "%s", pIx->zName));
-#ifdef SQLITE_ENABLE_COLUMN_USED_MASK
-        {
-          u64 colUsed = 0;
-          int ii, jj;
-          for(ii=0; ii<pIx->nColumn; ii++){
-            jj = pIx->aiColumn[ii];
-            if( jj<0 ) continue;
-            if( jj>63 ) jj = 63;
-            if( (pTabItem->colUsed & MASKBIT(jj))==0 ) continue;
-            colUsed |= ((u64)1)<<(ii<63 ? ii : 63);
-          }
-          sqlite3VdbeAddOp4Dup8(v, OP_ColumnsUsed, iIndexCur, 0, 0,
-                                (u8*)&colUsed, P4_INT64);
-        }
-#endif /* SQLITE_ENABLE_COLUMN_USED_MASK */
-      }
-    }
-    if( iDb>=0 ) sqlite3CodeVerifySchema(pParse, iDb);
-  }
-  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++){
-    int addrExplain;
-    int wsFlags;
-    pLevel = &pWInfo->a[ii];
-    wsFlags = pLevel->pWLoop->wsFlags;
-#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
-    addrExplain = sqlite3WhereExplainOneScan(
-        pParse, pTabList, pLevel, ii, pLevel->iFrom, wctrlFlags
-    );
-    pLevel->addrBody = sqlite3VdbeCurrentAddr(v);
-    notReady = sqlite3WhereCodeOneLoopStart(pWInfo, ii, notReady);
-    pWInfo->iContinue = pLevel->addrCont;
-    if( (wsFlags&WHERE_MULTI_OR)==0 && (wctrlFlags&WHERE_ONETABLE_ONLY)==0 ){
-      sqlite3WhereAddScanStatus(v, pTabList, pLevel, addrExplain);
-    }
-  }
-
-  /* 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);
-      }
-    }
-    sqlite3VdbeResolveLabel(v, pLevel->addrBrk);
-    if( pLevel->addrSkip ){
-      sqlite3VdbeGoto(v, 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->addrLikeRep ){
-      int op;
-      if( sqlite3VdbeGetOp(v, pLevel->addrLikeRep-1)->p1 ){
-        op = OP_DecrJumpZero;
-      }else{
-        op = OP_JumpZeroIncr;
-      }
-      sqlite3VdbeAddOp2(v, op, pLevel->iLikeRepCntr, pLevel->addrLikeRep);
-      VdbeCoverage(v);
-    }
-    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{
-        sqlite3VdbeGoto(v, 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_Copy of result contained in a register.
-    ** OP_Rowid becomes OP_Null.
-    */
-    if( pTabItem->fg.viaCoroutine && !db->mallocFailed ){
-      translateColumnToCopy(v, pLevel->addrBody, pLevel->iTabCur,
-                            pTabItem->regResult, 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->eOnePass==ONEPASS_OFF && (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
-     && (pWInfo->eOnePass==ONEPASS_OFF || !HasRowid(pIdx->pTable))
-     && !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];
-            assert( x>=0 );
-          }
-          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;
-}