SQLite: Artifact [2ea91123]

Artifact 2ea911238674e9baaeddf105dddabed92692a01996073c4d4983f9a7efe481f9:

File src/where.c — part of check-in [c1ea0649] at 2020-07-16 18:55:58 on branch trunk — Relax pointless restrictions on allowing tables in the FROM clause from crossing over LEFT JOINs, as long as the table being moved is not the right table of the LEFT JOIN. (user: drh size: 208702) [more...]
/*
** 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"

/*
** Extra information appended to the end of sqlite3_index_info but not
** visible to the xBestIndex function, at least not directly.  The
** sqlite3_vtab_collation() interface knows how to reach it, however.
**
** This object is not an API and can be changed from one release to the
** next.  As long as allocateIndexInfo() and sqlite3_vtab_collation()
** agree on the structure, all will be well.
*/
typedef struct HiddenIndexInfo HiddenIndexInfo;
struct HiddenIndexInfo {
  WhereClause *pWC;   /* The Where clause being analyzed */
  Parse *pParse;      /* The parsing context */
};

/* 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
*/
LogEst sqlite3WhereOutputRowCount(WhereInfo *pWInfo){
  return 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 the number of ORDER BY terms that are satisfied by the
** WHERE clause.  A return of 0 means that the output must be
** completely sorted.  A return equal to the number of ORDER BY
** terms means that no sorting is needed at all.  A return that
** is positive but less than the number of ORDER BY terms means that
** block sorting is required.
*/
int sqlite3WhereIsOrdered(WhereInfo *pWInfo){
  return pWInfo->nOBSat;
}

/*
** In the ORDER BY LIMIT optimization, if the inner-most loop is known
** to emit rows in increasing order, and if the last row emitted by the
** inner-most loop did not fit within the sorter, then we can skip all
** subsequent rows for the current iteration of the inner loop (because they
** will not fit in the sorter either) and continue with the second inner
** loop - the loop immediately outside the inner-most.
**
** When a row does not fit in the sorter (because the sorter already
** holds LIMIT+OFFSET rows that are smaller), then a jump is made to the
** label returned by this function.
**
** If the ORDER BY LIMIT optimization applies, the jump destination should
** be the continuation for the second-inner-most loop.  If the ORDER BY
** LIMIT optimization does not apply, then the jump destination should
** be the continuation for the inner-most loop.
**
** It is always safe for this routine to return the continuation of the
** inner-most loop, in the sense that a correct answer will result.  
** Returning the continuation the second inner loop is an optimization
** that might make the code run a little faster, but should not change
** the final answer.
*/
int sqlite3WhereOrderByLimitOptLabel(WhereInfo *pWInfo){
  WhereLevel *pInner;
  if( !pWInfo->bOrderedInnerLoop ){
    /* The ORDER BY LIMIT optimization does not apply.  Jump to the 
    ** continuation of the inner-most loop. */
    return pWInfo->iContinue;
  }
  pInner = &pWInfo->a[pWInfo->nLevel-1];
  assert( pInner->addrNxt!=0 );
  return pInner->addrNxt;
}

/*
** 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 rowids 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;
}

/*
** Return TRUE if the WHERE loop uses the OP_DeferredSeek opcode to move
** the data cursor to the row selected by the index cursor.
*/
int sqlite3WhereUsesDeferredSeek(WhereInfo *pWInfo){
  return pWInfo->bDeferredSeek;
}

/*
** 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 */

  assert( pScan->iEquiv<=pScan->nEquiv );
  pWC = pScan->pWC;
  while(1){
    iColumn = pScan->aiColumn[pScan->iEquiv-1];
    iCur = pScan->aiCur[pScan->iEquiv-1];
    assert( pWC!=0 );
    do{
      for(pTerm=pWC->a+k; k<pWC->nTerm; k++, pTerm++){
        if( pTerm->leftCursor==iCur
         && pTerm->u.leftColumn==iColumn
         && (iColumn!=XN_EXPR
             || sqlite3ExprCompareSkip(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 = sqlite3ExprSkipCollateAndLikely(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 = sqlite3ExprCompareCollSeq(pParse, pX);
              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->pWC = pWC;
            pScan->k = k+1;
            return pTerm;
          }
        }
      }
      pWC = pWC->pOuter;
      k = 0;
    }while( pWC!=0 );
    if( pScan->iEquiv>=pScan->nEquiv ) break;
    pWC = pScan->pOrigWC;
    k = 0;
    pScan->iEquiv++;
  }
  return 0;
}

/*
** This is whereScanInit() for the case of an index on an expression.
** It is factored out into a separate tail-recursion subroutine so that
** the normal whereScanInit() routine, which is a high-runner, does not
** need to push registers onto the stack as part of its prologue.
*/
static SQLITE_NOINLINE WhereTerm *whereScanInitIndexExpr(WhereScan *pScan){
  pScan->idxaff = sqlite3ExprAffinity(pScan->pIdxExpr);
  return whereScanNext(pScan);
}

/*
** 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.   Or if pIdx!=0 then X is column iColumn of index pIdx.  pIdx
** must be one of the indexes 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 */
){
  pScan->pOrigWC = pWC;
  pScan->pWC = pWC;
  pScan->pIdxExpr = 0;
  pScan->idxaff = 0;
  pScan->zCollName = 0;
  pScan->opMask = opMask;
  pScan->k = 0;
  pScan->aiCur[0] = iCur;
  pScan->nEquiv = 1;
  pScan->iEquiv = 1;
  if( pIdx ){
    int j = iColumn;
    iColumn = pIdx->aiColumn[j];
    if( iColumn==XN_EXPR ){
      pScan->pIdxExpr = pIdx->aColExpr->a[j].pExpr;
      pScan->zCollName = pIdx->azColl[j];
      pScan->aiColumn[0] = XN_EXPR;
      return whereScanInitIndexExpr(pScan);
    }else if( iColumn==pIdx->pTable->iPKey ){
      iColumn = XN_ROWID;
    }else if( iColumn>=0 ){
      pScan->idxaff = pIdx->pTable->aCol[iColumn].affinity;
      pScan->zCollName = pIdx->azColl[j];
    }
  }else if( iColumn==XN_EXPR ){
    return 0;
  }
  pScan->aiColumn[0] = iColumn;
  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 or of index pIdx
** if pIdx!=0 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 it must be one of the indexes of table iCur.  
** 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 = sqlite3ExprSkipCollateAndLikely(pList->a[i].pExpr);
    if( p->op==TK_COLUMN
     && p->iColumn==pIdx->aiColumn[iCol]
     && p->iTable==iBase
    ){
      CollSeq *pColl = sqlite3ExprNNCollSeq(pParse, pList->a[i].pExpr);
      if( 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 = sqlite3ExprSkipCollateAndLikely(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 iAutoidxCur is not zero, then any OP_Rowid instructions on
** cursor iTabCur are transformed into OP_Sequence opcode for the
** iAutoidxCur cursor, in order to generate unique rowids for the
** automatic index being generated.
*/
static void translateColumnToCopy(
  Parse *pParse,      /* Parsing context */
  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 iAutoidxCur     /* If non-zero, cursor of autoindex being generated */
){
  Vdbe *v = pParse->pVdbe;
  VdbeOp *pOp = sqlite3VdbeGetOp(v, iStart);
  int iEnd = sqlite3VdbeCurrentAddr(v);
  if( pParse->db->mallocFailed ) return;
  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( iAutoidxCur ){
        pOp->opcode = OP_Sequence;
        pOp->p1 = iAutoidxCur;
      }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 whereTraceIndexInfoInputs(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 whereTraceIndexInfoOutputs(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 whereTraceIndexInfoInputs(A)
#define whereTraceIndexInfoOutputs(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( (pSrc->fg.jointype & JT_LEFT) 
   && !ExprHasProperty(pTerm->pExpr, EP_FromJoin)
   && (pTerm->eOperator & WO_IS)
  ){
    /* Cannot use an IS term from the WHERE clause as an index driver for
    ** the RHS of a LEFT JOIN. Such a term can only be used if it is from
    ** the ON clause.  */
    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 = 0;        /* 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 = sqlite3VdbeAddOp0(v, OP_Once); 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, 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 = sqlite3ExprCompareCollSeq(pParse, pX);
        assert( pColl!=0 || pParse->nErr>0 ); /* TH3 collate01.800 */
        pIdx->azColl[n] = pColl ? pColl->zName : sqlite3StrBINARY;
        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] = sqlite3StrBINARY;
      n++;
    }
  }
  if( pSrc->colUsed & MASKBIT(BMS-1) ){
    for(i=BMS-1; i<pTable->nCol; i++){
      pIdx->aiColumn[n] = i;
      pIdx->azColl[n] = sqlite3StrBINARY;
      n++;
    }
  }
  assert( n==nKeyCol );
  pIdx->aiColumn[n] = XN_ROWID;
  pIdx->azColl[n] = sqlite3StrBINARY;

  /* 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 */
  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(pParse);
    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);
    testcase( pParse->db->mallocFailed );
    assert( pLevel->iIdxCur>0 );
    translateColumnToCopy(pParse, addrTop, pLevel->iTabCur,
                          pTabItem->regResult, pLevel->iIdxCur);
    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);
  
  /* 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,                  /* The parsing context */
  WhereClause *pWC,               /* The WHERE clause being analyzed */
  Bitmask mUnusable,              /* Ignore terms with these prereqs */
  struct SrcList_item *pSrc,      /* The FROM clause term that is the vtab */
  ExprList *pOrderBy,             /* The ORDER BY clause */
  u16 *pmNoOmit                   /* Mask of terms not to omit */
){
  int i, j;
  int nTerm;
  struct sqlite3_index_constraint *pIdxCons;
  struct sqlite3_index_orderby *pIdxOrderBy;
  struct sqlite3_index_constraint_usage *pUsage;
  struct HiddenIndexInfo *pHidden;
  WhereTerm *pTerm;
  int nOrderBy;
  sqlite3_index_info *pIdxInfo;
  u16 mNoOmit = 0;

  /* 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_EQUIV))==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( pOrderBy->a[i].sortFlags & KEYINFO_ORDER_BIGNULL ) 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 + sizeof(*pHidden) );
  if( pIdxInfo==0 ){
    sqlite3ErrorMsg(pParse, "out of memory");
    return 0;
  }
  pHidden = (struct HiddenIndexInfo*)&pIdxInfo[1];
  pIdxCons = (struct sqlite3_index_constraint*)&pHidden[1];
  pIdxOrderBy = (struct sqlite3_index_orderby*)&pIdxCons[nTerm];
  pUsage = (struct sqlite3_index_constraint_usage*)&pIdxOrderBy[nOrderBy];
  pIdxInfo->nOrderBy = nOrderBy;
  pIdxInfo->aConstraint = pIdxCons;
  pIdxInfo->aOrderBy = pIdxOrderBy;
  pIdxInfo->aConstraintUsage = pUsage;
  pHidden->pWC = pWC;
  pHidden->pParse = pParse;
  for(i=j=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
    u16 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_EQUIV))==0 ) continue;
    if( pTerm->wtFlags & TERM_VNULL ) continue;

    /* tag-20191211-002: WHERE-clause constraints are not useful to the
    ** right-hand table of a LEFT JOIN.  See tag-20191211-001 for the
    ** equivalent restriction for ordinary tables. */
    if( (pSrc->fg.jointype & JT_LEFT)!=0
     && !ExprHasProperty(pTerm->pExpr, EP_FromJoin)
    ){
      continue;
    }
    assert( pTerm->u.leftColumn>=(-1) );
    pIdxCons[j].iColumn = pTerm->u.leftColumn;
    pIdxCons[j].iTermOffset = i;
    op = pTerm->eOperator & WO_ALL;
    if( op==WO_IN ) op = WO_EQ;
    if( op==WO_AUX ){
      pIdxCons[j].op = pTerm->eMatchOp;
    }else if( op & (WO_ISNULL|WO_IS) ){
      if( op==WO_ISNULL ){
        pIdxCons[j].op = SQLITE_INDEX_CONSTRAINT_ISNULL;
      }else{
        pIdxCons[j].op = SQLITE_INDEX_CONSTRAINT_IS;
      }
    }else{
      pIdxCons[j].op = (u8)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( pTerm->eOperator&(WO_IN|WO_EQ|WO_LT|WO_LE|WO_GT|WO_GE|WO_AUX) );

      if( op & (WO_LT|WO_LE|WO_GT|WO_GE)
       && sqlite3ExprIsVector(pTerm->pExpr->pRight) 
      ){
        testcase( j!=i );
        if( j<16 ) mNoOmit |= (1 << j);
        if( op==WO_LT ) pIdxCons[j].op = WO_LE;
        if( op==WO_GT ) pIdxCons[j].op = WO_GE;
      }
    }

    j++;
  }
  pIdxInfo->nConstraint = j;
  for(i=0; i<nOrderBy; i++){
    Expr *pExpr = pOrderBy->a[i].pExpr;
    pIdxOrderBy[i].iColumn = pExpr->iColumn;
    pIdxOrderBy[i].desc = pOrderBy->a[i].sortFlags & KEYINFO_ORDER_DESC;
  }

  *pmNoOmit = mNoOmit;
  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 an
** appropriate error code is returned.  A return of SQLITE_CONSTRAINT from
** xBestIndex is not considered an error.  SQLITE_CONSTRAINT indicates that
** the current configuration of "unusable" flags in sqlite3_index_info can
** not result in a valid plan.
**
** 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 rc;

  whereTraceIndexInfoInputs(p);
  rc = pVtab->pModule->xBestIndex(pVtab, p);
  whereTraceIndexInfoOutputs(p);

  if( rc!=SQLITE_OK && rc!=SQLITE_CONSTRAINT ){
    if( rc==SQLITE_NOMEM ){
      sqlite3OomFault(pParse->db);
    }else if( !pVtab->zErrMsg ){
      sqlite3ErrorMsg(pParse, "%s", sqlite3ErrStr(rc));
    }else{
      sqlite3ErrorMsg(pParse, "%s", pVtab->zErrMsg);
    }
  }
  sqlite3_free(pVtab->zErrMsg);
  pVtab->zErrMsg = 0;
  return rc;
}
#endif /* !defined(SQLITE_OMIT_VIRTUALTABLE) */

#ifdef SQLITE_ENABLE_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[nField-1];
  }

  /* Restore the pRec->nField value before returning.  */
  pRec->nField = nField;
  return i;
}
#endif /* SQLITE_ENABLE_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_STAT4
/*
** Return the affinity for a single column of an index.
*/
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;
  }
  assert( pIdx->zColAff[iCol]!=0 );
  return pIdx->zColAff[iCol];
}
#endif


#ifdef SQLITE_ENABLE_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_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_STAT4
  Index *p = pLoop->u.btree.pIndex;
  int nEq = pLoop->u.btree.nEq;

  if( p->nSample>0 && ALWAYS(nEq<p->nSampleCol)
   && OptimizationEnabled(pParse->db, SQLITE_Stat4)
  ){
    if( nEq==pBuilder->nRecValid ){
      UnpackedRecord *pRec = pBuilder->pRec;
      tRowcnt a[2];
      int nBtm = pLoop->u.btree.nBtm;
      int nTop = pLoop->u.btree.nTop;

      /* 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;
      }
      /* 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);
        SWAP(int, nBtm, nTop);
      }

      /* If possible, improve on the iLower estimate using ($P:$L). */
      if( pLower ){
        int n;                    /* Values extracted from pExpr */
        Expr *pExpr = pLower->pExpr->pRight;
        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, nBtm, nEq, &n);
        if( rc==SQLITE_OK && n ){
          tRowcnt iNew;
          u16 mask = WO_GT|WO_LE;
          if( sqlite3ExprVectorSize(pExpr)>n ) mask = (WO_LE|WO_LT);
          iLwrIdx = whereKeyStats(pParse, p, pRec, 0, a);
          iNew = a[0] + ((pLower->eOperator & mask) ? a[1] : 0);
          if( iNew>iLower ) iLower = iNew;
          nOut--;
          pLower = 0;
        }
      }

      /* If possible, improve on the iUpper estimate using ($P:$U). */
      if( pUpper ){
        int n;                    /* Values extracted from pExpr */
        Expr *pExpr = pUpper->pExpr->pRight;
        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, nTop, nEq, &n);
        if( rc==SQLITE_OK && n ){
          tRowcnt iNew;
          u16 mask = WO_GT|WO_LE;
          if( sqlite3ExprVectorSize(pExpr)>n ) mask = (WO_LE|WO_LT);
          iUprIdx = whereKeyStats(pParse, p, pRec, 1, a);
          iNew = a[0] + ((pUpper->eOperator & mask) ? 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 STAT4 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_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_stat4 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;
  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;
  }

  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, 1, 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 %s(%d): %d\n",
                   p->zName, nEq-1, (int)a[1]));
  *pnRow = a[1];
  
  return rc;
}
#endif /* SQLITE_ENABLE_STAT4 */

#ifdef SQLITE_ENABLE_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_STAT4 */


#ifdef WHERETRACE_ENABLED
/*
** Print the content of a WhereTerm object
*/
void sqlite3WhereTermPrint(WhereTerm *pTerm, int iTerm){
  if( pTerm==0 ){
    sqlite3DebugPrintf("TERM-%-3d NULL\n", iTerm);
  }else{
    char zType[8];
    char zLeft[50];
    memcpy(zType, "....", 5);
    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';
    if( pTerm->wtFlags & TERM_CODED  ) zType[3] = 'C';
    if( pTerm->eOperator & WO_SINGLE ){
      sqlite3_snprintf(sizeof(zLeft),zLeft,"left={%d:%d}",
                       pTerm->leftCursor, pTerm->u.leftColumn);
    }else if( (pTerm->eOperator & WO_OR)!=0 && pTerm->u.pOrInfo!=0 ){
      sqlite3_snprintf(sizeof(zLeft),zLeft,"indexable=0x%lld", 
                       pTerm->u.pOrInfo->indexable);
    }else{
      sqlite3_snprintf(sizeof(zLeft),zLeft,"left=%d", pTerm->leftCursor);
    }
    sqlite3DebugPrintf(
       "TERM-%-3d %p %s %-12s op=%03x wtFlags=%04x",
       iTerm, pTerm, zType, zLeft, pTerm->eOperator, pTerm->wtFlags);
    /* The 0x10000 .wheretrace flag causes extra information to be
    ** shown about each Term */
    if( sqlite3WhereTrace & 0x10000 ){
      sqlite3DebugPrintf(" prob=%-3d prereq=%llx,%llx",
        pTerm->truthProb, (u64)pTerm->prereqAll, (u64)pTerm->prereqRight);
    }
    if( pTerm->iField ){
      sqlite3DebugPrintf(" iField=%d", pTerm->iField);
    }
    if( pTerm->iParent>=0 ){
      sqlite3DebugPrintf(" iParent=%d", pTerm->iParent);
    }
    sqlite3DebugPrintf("\n");
    sqlite3TreeViewExpr(0, pTerm->pExpr, 0);
  }
}
#endif

#ifdef WHERETRACE_ENABLED
/*
** Show the complete content of a WhereClause
*/
void sqlite3WhereClausePrint(WhereClause *pWC){
  int i;
  for(i=0; i<pWC->nTerm; i++){
    sqlite3WhereTermPrint(&pWC->a[i], i);
  }
}
#endif

#ifdef WHERETRACE_ENABLED
/*
** Print a WhereLoop object for debugging purposes
*/
void sqlite3WhereLoopPrint(WhereLoop *p, WhereClause *pWC){
  WhereInfo *pWInfo = pWC->pWInfo;
  int nb = 1+(pWInfo->pTabList->nSrc+3)/4;
  struct SrcList_item *pItem = pWInfo->pTabList->a + p->iTab;
  Table *pTab = pItem->pTab;
  Bitmask mAll = (((Bitmask)1)<<(nb*4)) - 1;
  sqlite3DebugPrintf("%c%2d.%0*llx.%0*llx", p->cId,
                     p->iTab, nb, p->maskSelf, nb, p->prereq & mAll);
  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++){
      sqlite3WhereTermPrint(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);
      sqlite3DbFreeNN(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 ) sqlite3DbFreeNN(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 = sqlite3DbMallocRawNN(db, sizeof(p->aLTerm[0])*n);
  if( paNew==0 ) return SQLITE_NOMEM_BKPT;
  memcpy(paNew, p->aLTerm, sizeof(p->aLTerm[0])*p->nLSlot);
  if( p->aLTerm!=p->aLTermSpace ) sqlite3DbFreeNN(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_BKPT;
  }
  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);
  sqlite3DbFreeNN(db, p);
}

/*
** Free a WhereInfo structure
*/
static void whereInfoFree(sqlite3 *db, WhereInfo *pWInfo){
  int i;
  assert( pWInfo!=0 );
  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);
  }
  assert( pWInfo->pExprMods==0 );
  sqlite3DbFreeNN(db, pWInfo);
}

/*
** Return TRUE if all of the following are true:
**
**   (1)  X has the same or lower cost that Y
**   (2)  X uses fewer WHERE clause terms than Y
**   (3)  Every WHERE clause term used by X is also used by Y
**   (4)  X skips at least as many columns as Y
**   (5)  If X is a covering index, than Y is too
**
** Conditions (2) and (3) mean that X is a "proper subset" of 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.  Constraint (4)
** 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.  Constraint (5)
** was added because a covering index probably deserves to have a lower cost
** than a non-covering index even if it is a proper subset.
*/
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 */
  }
  if( (pX->wsFlags&WHERE_IDX_ONLY)!=0 
   && (pY->wsFlags&WHERE_IDX_ONLY)==0 ){
    return 0;  /* Constraint (5) */
  }
  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
** replaced by pTemplate.
**
** Return NULL if pTemplate does not belong on the WhereLoop list.
** In other words if pTemplate ought to be dropped from further consideration.
**
** If pX is a WhereLoop that pTemplate can replace, then return the
** link that points to pX.
**
** If pTemplate cannot replace any existing element of the list but needs
** to be added to the list as a new entry, 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;
  int rc;

  /* Stop the search once we hit the query planner search limit */
  if( pBuilder->iPlanLimit==0 ){
    WHERETRACE(0xffffffff,("=== query planner search limit reached ===\n"));
    if( pBuilder->pOrSet ) pBuilder->pOrSet->n = 0;
    return SQLITE_DONE;
  }
  pBuilder->iPlanLimit--;

  whereLoopAdjustCost(pWInfo->pLoops, pTemplate);

  /* 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);
        sqlite3WhereLoopPrint(pTemplate, pBuilder->pWC);
      }
#endif
    }
    return SQLITE_OK;
  }

  /* Look for an existing WhereLoop to replace with 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: ");
      sqlite3WhereLoopPrint(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: ");
      sqlite3WhereLoopPrint(p, pBuilder->pWC);
      sqlite3DebugPrintf("   with: ");
    }else{
      sqlite3DebugPrintf("    add: ");
    }
    sqlite3WhereLoopPrint(pTemplate, pBuilder->pWC);
  }
#endif
  if( p==0 ){
    /* Allocate a new WhereLoop to add to the end of the list */
    *ppPrev = p = sqlite3DbMallocRawNN(db, sizeof(WhereLoop));
    if( p==0 ) return SQLITE_NOMEM_BKPT;
    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: ");
        sqlite3WhereLoopPrint(pToDel, pBuilder->pWC);
      }
#endif
      whereLoopDelete(db, pToDel);
    }
  }
  rc = whereLoopXfer(db, p, pTemplate);
  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){
    Index *pIndex = p->u.btree.pIndex;
    if( pIndex && pIndex->idxType==SQLITE_IDXTYPE_IPK ){
      p->u.btree.pIndex = 0;
    }
  }
  return rc;
}

/*
** 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;
  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++){
    assert( pTerm!=0 );
    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))!=0
         && (pTerm->wtFlags & TERM_HIGHTRUTH)==0  /* tag-20200224-1 */
        ){
          Expr *pRight = pTerm->pExpr->pRight;
          int k = 0;
          testcase( pTerm->pExpr->op==TK_IS );
          if( sqlite3ExprIsInteger(pRight, &k) && k>=(-1) && k<=1 ){
            k = 10;
          }else{
            k = 20;
          }
          if( iReduce<k ){
            pTerm->wtFlags |= TERM_HEURTRUTH;
            iReduce = k;
          }
        }
      }
    }
  }
  if( pLoop->nOut > nRow-iReduce )  pLoop->nOut = nRow - iReduce;
}

/* 
** Term pTerm is a vector range comparison operation. The first comparison
** in the vector can be optimized using column nEq of the index. This
** function returns the total number of vector elements that can be used
** as part of the range comparison.
**
** For example, if the query is:
**
**   WHERE a = ? AND (b, c, d) > (?, ?, ?)
**
** and the index:
**
**   CREATE INDEX ... ON (a, b, c, d, e)
**
** then this function would be invoked with nEq=1. The value returned in
** this case is 3.
*/
static int whereRangeVectorLen(
  Parse *pParse,       /* Parsing context */
  int iCur,            /* Cursor open on pIdx */
  Index *pIdx,         /* The index to be used for a inequality constraint */
  int nEq,             /* Number of prior equality constraints on same index */
  WhereTerm *pTerm     /* The vector inequality constraint */
){
  int nCmp = sqlite3ExprVectorSize(pTerm->pExpr->pLeft);
  int i;

  nCmp = MIN(nCmp, (pIdx->nColumn - nEq));
  for(i=1; i<nCmp; i++){
    /* Test if comparison i of pTerm is compatible with column (i+nEq) 
    ** of the index. If not, exit the loop.  */
    char aff;                     /* Comparison affinity */
    char idxaff = 0;              /* Indexed columns affinity */
    CollSeq *pColl;               /* Comparison collation sequence */
    Expr *pLhs = pTerm->pExpr->pLeft->x.pList->a[i].pExpr;
    Expr *pRhs = pTerm->pExpr->pRight;
    if( pRhs->flags & EP_xIsSelect ){
      pRhs = pRhs->x.pSelect->pEList->a[i].pExpr;
    }else{
      pRhs = pRhs->x.pList->a[i].pExpr;
    }

    /* Check that the LHS of the comparison is a column reference to
    ** the right column of the right source table. And that the sort
    ** order of the index column is the same as the sort order of the
    ** leftmost index column.  */
    if( pLhs->op!=TK_COLUMN 
     || pLhs->iTable!=iCur 
     || pLhs->iColumn!=pIdx->aiColumn[i+nEq] 
     || pIdx->aSortOrder[i+nEq]!=pIdx->aSortOrder[nEq]
    ){
      break;
    }

    testcase( pLhs->iColumn==XN_ROWID );
    aff = sqlite3CompareAffinity(pRhs, sqlite3ExprAffinity(pLhs));
    idxaff = sqlite3TableColumnAffinity(pIdx->pTable, pLhs->iColumn);
    if( aff!=idxaff ) break;

    pColl = sqlite3BinaryCompareCollSeq(pParse, pLhs, pRhs);
    if( pColl==0 ) break;
    if( sqlite3StrICmp(pColl->zName, pIdx->azColl[i+nEq]) ) break;
  }
  return i;
}

/*
** 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->idxType==SQLITE_IDXTYPE_IPK, 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_nBtm;                 /* Original value of pNew->u.btree.nBtm */
  u16 saved_nTop;                 /* Original value of pNew->u.btree.nTop */
  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_BKPT;
  WHERETRACE(0x800, ("BEGIN %s.addBtreeIdx(%s), nEq=%d, nSkip=%d\n",
                     pProbe->pTable->zName,pProbe->zName,
                     pNew->u.btree.nEq, pNew->nSkip));

  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{
    assert( pNew->u.btree.nBtm==0 );
    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_nBtm = pNew->u.btree.nBtm;
  saved_nTop = pNew->u.btree.nTop;
  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_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;

    /* tag-20191211-001:  Do not allow constraints from the WHERE clause to
    ** be used by the right table of a LEFT JOIN.  Only constraints in the
    ** ON clause are allowed.  See tag-20191211-002 for the vtab equivalent. */
    if( (pSrc->fg.jointype & JT_LEFT)!=0
     && !ExprHasProperty(pTerm->pExpr, EP_FromJoin)
    ){
      continue;
    }

    if( IsUniqueIndex(pProbe) && saved_nEq==pProbe->nKeyCol-1 ){
      pBuilder->bldFlags1 |= SQLITE_BLDF1_UNIQUE;
    }else{
      pBuilder->bldFlags1 |= SQLITE_BLDF1_INDEXED;
    }
    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->u.btree.nBtm = saved_nBtm;
    pNew->u.btree.nTop = saved_nTop;
    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;
      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
        /* "x IN (SELECT ...)":  TUNING: the SELECT returns 25 rows */
        int i;
        nIn = 46;  assert( 46==sqlite3LogEst(25) );

        /* The expression may actually be of the form (x, y) IN (SELECT...).
        ** In this case there is a separate term for each of (x) and (y).
        ** However, the nIn multiplier should only be applied once, not once
        ** for each such term. The following loop checks that pTerm is the
        ** first such term in use, and sets nIn back to 0 if it is not. */
        for(i=0; i<pNew->nLTerm-1; i++){
          if( pNew->aLTerm[i] && pNew->aLTerm[i]->pExpr==pExpr ) nIn = 0;
        }
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = sqlite3LogEst(pExpr->x.pList->nExpr);
      }
      if( pProbe->hasStat1 ){
        LogEst M, logK, safetyMargin;
        /* Let:
        **   N = the total number of rows in the table
        **   K = the number of entries on the RHS of the IN operator
        **   M = the number of rows in the table that match terms to the 
        **       to the left in the same index.  If the IN operator is on
        **       the left-most index column, M==N.
        **
        ** Given the definitions above, it is better to omit the IN operator
        ** from the index lookup and instead do a scan of the M elements,
        ** testing each scanned row against the IN operator separately, if:
        **
        **        M*log(K) < K*log(N)
        **
        ** Our estimates for M, K, and N might be inaccurate, so we build in
        ** a safety margin of 2 (LogEst: 10) that favors using the IN operator
        ** with the index, as using an index has better worst-case behavior.
        ** If we do not have real sqlite_stat1 data, always prefer to use
        ** the index.
        */
        M = pProbe->aiRowLogEst[saved_nEq];
        logK = estLog(nIn);
        safetyMargin = 10;  /* TUNING: extra weight for indexed IN */
        if( M + logK + safetyMargin < nIn + rLogSize ){
          WHERETRACE(0x40,
            ("Scan preferred over IN operator on column %d of \"%s\" (%d<%d)\n",
             saved_nEq, pProbe->zName, M+logK+10, nIn+rLogSize));
          continue;
        }else{
          WHERETRACE(0x40,
            ("IN operator preferred on column %d of \"%s\" (%d>=%d)\n",
             saved_nEq, pProbe->zName, M+logK+10, nIn+rLogSize));
        }
      }
      pNew->wsFlags |= WHERE_COLUMN_IN;
    }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==XN_ROWID || pProbe->uniqNotNull 
         || (pProbe->nKeyCol==1 && pProbe->onError && eOp==WO_EQ) 
        ){
          pNew->wsFlags |= WHERE_ONEROW;
        }else{
          pNew->wsFlags |= WHERE_UNQ_WANTED;
        }
      }
    }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;
      pNew->u.btree.nBtm = whereRangeVectorLen(
          pParse, pSrc->iCursor, pProbe, saved_nEq, pTerm
      );
      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;
        pNew->u.btree.nTop = 1;
      }
    }else{
      assert( eOp & (WO_LT|WO_LE) );
      testcase( eOp & WO_LT );
      testcase( eOp & WO_LE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pNew->u.btree.nTop = whereRangeVectorLen(
          pParse, pSrc->iCursor, pProbe, saved_nEq, pTerm
      );
      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 stat4 data. Or, if there is no 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_STAT4
        tRowcnt nOut = 0;
        if( nInMul==0 
         && pProbe->nSample 
         && pNew->u.btree.nEq<=pProbe->nSampleCol
         && ((eOp & WO_IN)==0 || !ExprHasProperty(pTerm->pExpr, EP_xIsSelect))
         && OptimizationEnabled(db, SQLITE_Stat4)
        ){
          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( nEq==1
             /* TUNING: Mark terms as "low selectivity" if they seem likely
             ** to be true for half or more of the rows in the table.
             ** See tag-202002240-1 */
             && pNew->nOut+10 > pProbe->aiRowLogEst[0]
            ){
#if WHERETRACE_ENABLED /* 0x01 */
              if( sqlite3WhereTrace & 0x01 ){
                sqlite3DebugPrintf(
                   "STAT4 determines term has low selectivity:\n");
                sqlite3WhereTermPrint(pTerm, 999);
              }
#endif
              pTerm->wtFlags |= TERM_HIGHTRUTH;
              if( pTerm->wtFlags & TERM_HEURTRUTH ){
                /* If the term has previously been used with an assumption of
                ** higher selectivity, then set the flag to rerun the
                ** loop computations. */
                pBuilder->bldFlags2 |= SQLITE_BLDF2_2NDPASS;
              }
            }
            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.  */
    assert( pSrc->pTab->szTabRow>0 );
    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_STAT4
    pBuilder->nRecValid = nRecValid;
#endif
  }
  pNew->prereq = saved_prereq;
  pNew->u.btree.nEq = saved_nEq;
  pNew->u.btree.nBtm = saved_nBtm;
  pNew->u.btree.nTop = saved_nTop;
  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
   && saved_nEq==pNew->nLTerm
   && pProbe->noSkipScan==0
   && pProbe->hasStat1!=0
   && OptimizationEnabled(db, SQLITE_SkipScan)
   && 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;
  }

  WHERETRACE(0x800, ("END %s.addBtreeIdx(%s), nEq=%d, rc=%d\n",
                      pProbe->pTable->zName, pProbe->zName, saved_nEq, rc));
  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 = sqlite3ExprSkipCollateAndLikely(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( sqlite3ExprCompareSkip(pExpr,aColExpr->a[jj].pExpr,iCursor)==0 ){
          return 1;
        }
      }
    }
  }
  return 0;
}

/* 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,             /* The table for which we want an index */
  int isLeft,           /* True if iTab is the right table of a LEFT JOIN */
  WhereClause *pWC,     /* The WHERE clause of the query */
  Expr *pWhere          /* The WHERE clause from the partial index */
){
  int i;
  WhereTerm *pTerm;
  Parse *pParse = pWC->pWInfo->pParse;
  while( pWhere->op==TK_AND ){
    if( !whereUsablePartialIndex(iTab,isLeft,pWC,pWhere->pLeft) ) return 0;
    pWhere = pWhere->pRight;
  }
  if( pParse->db->flags & SQLITE_EnableQPSG ) pParse = 0;
  for(i=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){
    Expr *pExpr;
    pExpr = pTerm->pExpr;
    if( (!ExprHasProperty(pExpr, EP_FromJoin) || pExpr->iRightJoinTable==iTab)
     && (isLeft==0 || ExprHasProperty(pExpr, EP_FromJoin))
     && sqlite3ExprImpliesExpr(pParse, pExpr, pWhere, iTab) 
    ){
      return 1;
    }
  }
  return 0;
}

/*
** Add all WhereLoop objects for a single table of the join where the table
** is identified 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 mPrereq             /* 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;
    sPk.idxType = SQLITE_IDXTYPE_IPK;
    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_OR_SUBCLAUSE)==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 0.5 (LogEst=-10) 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;
        if( pTab->pSelect==0 && (pTab->tabFlags & TF_Ephemeral)==0 ){
          pNew->rSetup += 28;
        }else{
          pNew->rSetup -= 10;
        }
        ApplyCostMultiplier(pNew->rSetup, pTab->costMult);
        if( pNew->rSetup<0 ) pNew->rSetup = 0;
        /* 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 = mPrereq | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */

  /* Loop over all indices. If there was an INDEXED BY clause, then only 
  ** consider index pProbe.  */
  for(; rc==SQLITE_OK && pProbe; 
      pProbe=(pSrc->pIBIndex ? 0 : pProbe->pNext), iSortIdx++
  ){
    int isLeft = (pSrc->fg.jointype & JT_OUTER)!=0;
    if( pProbe->pPartIdxWhere!=0
     && !whereUsablePartialIndex(pSrc->iCursor, isLeft, pWC,
                                 pProbe->pPartIdxWhere)
    ){
      testcase( pNew->iTab!=pSrc->iCursor );  /* See ticket [98d973b8f5] */
      continue;  /* Partial index inappropriate for this query */
    }
    if( pProbe->bNoQuery ) continue;
    rSize = pProbe->aiRowLogEst[0];
    pNew->u.btree.nEq = 0;
    pNew->u.btree.nBtm = 0;
    pNew->u.btree.nTop = 0;
    pNew->nSkip = 0;
    pNew->nLTerm = 0;
    pNew->iSortIdx = 0;
    pNew->rSetup = 0;
    pNew->prereq = mPrereq;
    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->idxType==SQLITE_IDXTYPE_IPK ){
      /* 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 & pProbe->colNotIdxed;
        pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;
      }

      /* Full scan via index */
      if( b
       || !HasRowid(pTab)
       || pProbe->pPartIdxWhere!=0
       || pSrc->fg.isIndexedBy
       || ( 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. */
        pNew->rRun = rSize + 1 + (15*pProbe->szIdxRow)/pTab->szTabRow;
        if( m!=0 ){
          /* If this is a non-covering index scan, add in the cost of
          ** doing table lookups.  The cost will be 3x the number of
          ** lookups.  Take into account WHERE clause terms that can be
          ** satisfied using just the index, and that do not require a
          ** table lookup. */
          LogEst nLookup = rSize + 16;  /* Base cost:  N*3 */
          int ii;
          int iCur = pSrc->iCursor;
          WhereClause *pWC2 = &pWInfo->sWC;
          for(ii=0; ii<pWC2->nTerm; ii++){
            WhereTerm *pTerm = &pWC2->a[ii];
            if( !sqlite3ExprCoveredByIndex(pTerm->pExpr, iCur, pProbe) ){
              break;
            }
            /* pTerm can be evaluated using just the index.  So reduce
            ** the expected number of table lookups accordingly */
            if( pTerm->truthProb<=0 ){
              nLookup += pTerm->truthProb;
            }else{
              nLookup--;
              if( pTerm->eOperator & (WO_EQ|WO_IS) ) nLookup -= 19;
            }
          }
          
          pNew->rRun = sqlite3LogEstAdd(pNew->rRun, nLookup);
        }
        ApplyCostMultiplier(pNew->rRun, pTab->costMult);
        whereLoopOutputAdjust(pWC, pNew, rSize);
        rc = whereLoopInsert(pBuilder, pNew);
        pNew->nOut = rSize;
        if( rc ) break;
      }
    }

    pBuilder->bldFlags1 = 0;
    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);
    if( pBuilder->bldFlags1==SQLITE_BLDF1_INDEXED ){
      /* If a non-unique index is used, or if a prefix of the key for
      ** unique index is used (making the index functionally non-unique)
      ** then the sqlite_stat1 data becomes important for scoring the
      ** plan */
      pTab->tabFlags |= TF_StatsUsed;
    }
#ifdef SQLITE_ENABLE_STAT4
    sqlite3Stat4ProbeFree(pBuilder->pRec);
    pBuilder->nRecValid = 0;
    pBuilder->pRec = 0;
#endif
  }
  return rc;
}

#ifndef SQLITE_OMIT_VIRTUALTABLE

/*
** Argument pIdxInfo is already populated with all constraints that may
** be used by the virtual table identified by pBuilder->pNew->iTab. This
** function marks a subset of those constraints usable, invokes the
** xBestIndex method and adds the returned plan to pBuilder.
**
** A constraint is marked usable if:
**
**   * Argument mUsable indicates that its prerequisites are available, and
**
**   * It is not one of the operators specified in the mExclude mask passed
**     as the fourth argument (which in practice is either WO_IN or 0).
**
** Argument mPrereq is a mask of tables that must be scanned before the
** virtual table in question. These are added to the plans prerequisites
** before it is added to pBuilder.
**
** Output parameter *pbIn is set to true if the plan added to pBuilder
** uses one or more WO_IN terms, or false otherwise.
*/
static int whereLoopAddVirtualOne(
  WhereLoopBuilder *pBuilder,
  Bitmask mPrereq,                /* Mask of tables that must be used. */
  Bitmask mUsable,                /* Mask of usable tables */
  u16 mExclude,                   /* Exclude terms using these operators */
  sqlite3_index_info *pIdxInfo,   /* Populated object for xBestIndex */
  u16 mNoOmit,                    /* Do not omit these constraints */
  int *pbIn                       /* OUT: True if plan uses an IN(...) op */
){
  WhereClause *pWC = pBuilder->pWC;
  struct sqlite3_index_constraint *pIdxCons;
  struct sqlite3_index_constraint_usage *pUsage = pIdxInfo->aConstraintUsage;
  int i;
  int mxTerm;
  int rc = SQLITE_OK;
  WhereLoop *pNew = pBuilder->pNew;
  Parse *pParse = pBuilder->pWInfo->pParse;
  struct SrcList_item *pSrc = &pBuilder->pWInfo->pTabList->a[pNew->iTab];
  int nConstraint = pIdxInfo->nConstraint;

  assert( (mUsable & mPrereq)==mPrereq );
  *pbIn = 0;
  pNew->prereq = mPrereq;

  /* Set the usable flag on the subset of constraints identified by 
  ** arguments mUsable and mExclude. */
  pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
  for(i=0; i<nConstraint; i++, pIdxCons++){
    WhereTerm *pTerm = &pWC->a[pIdxCons->iTermOffset];
    pIdxCons->usable = 0;
    if( (pTerm->prereqRight & mUsable)==pTerm->prereqRight 
     && (pTerm->eOperator & mExclude)==0
    ){
      pIdxCons->usable = 1;
    }
  }

  /* Initialize the output fields of the sqlite3_index_info structure */
  memset(pUsage, 0, sizeof(pUsage[0])*nConstraint);
  assert( pIdxInfo->needToFreeIdxStr==0 );
  pIdxInfo->idxStr = 0;
  pIdxInfo->idxNum = 0;
  pIdxInfo->orderByConsumed = 0;
  pIdxInfo->estimatedCost = SQLITE_BIG_DBL / (double)2;
  pIdxInfo->estimatedRows = 25;
  pIdxInfo->idxFlags = 0;
  pIdxInfo->colUsed = (sqlite3_int64)pSrc->colUsed;

  /* Invoke the virtual table xBestIndex() method */
  rc = vtabBestIndex(pParse, pSrc->pTab, pIdxInfo);
  if( rc ){
    if( rc==SQLITE_CONSTRAINT ){
      /* If the xBestIndex method returns SQLITE_CONSTRAINT, that means
      ** that the particular combination of parameters provided is unusable.
      ** Make no entries in the loop table.
      */
      WHERETRACE(0xffff, ("  ^^^^--- non-viable plan rejected!\n"));
      return SQLITE_OK;
    }
    return rc;
  }

  mxTerm = -1;
  assert( pNew->nLSlot>=nConstraint );
  for(i=0; i<nConstraint; i++) pNew->aLTerm[i] = 0;
  pNew->u.vtab.omitMask = 0;
  pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;
  for(i=0; i<nConstraint; i++, pIdxCons++){
    int iTerm;
    if( (iTerm = pUsage[i].argvIndex - 1)>=0 ){
      WhereTerm *pTerm;
      int j = pIdxCons->iTermOffset;
      if( iTerm>=nConstraint
       || j<0
       || j>=pWC->nTerm
       || pNew->aLTerm[iTerm]!=0
       || pIdxCons->usable==0
      ){
        sqlite3ErrorMsg(pParse,"%s.xBestIndex malfunction",pSrc->pTab->zName);
        testcase( pIdxInfo->needToFreeIdxStr );
        return SQLITE_ERROR;
      }
      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( pUsage[i].omit ){
        if( i<16 && ((1<<i)&mNoOmit)==0 ){
          testcase( i!=iTerm );
          pNew->u.vtab.omitMask |= 1<<iTerm;
        }else{
          testcase( i!=iTerm );
        }
      }
      if( (pTerm->eOperator & WO_IN)!=0 ){
        /* 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;
        *pbIn = 1; assert( (mExclude & WO_IN)==0 );
      }
    }
  }

  pNew->nLTerm = mxTerm+1;
  for(i=0; i<=mxTerm; i++){
    if( pNew->aLTerm[i]==0 ){
      /* The non-zero argvIdx values must be contiguous.  Raise an
      ** error if they are not */
      sqlite3ErrorMsg(pParse,"%s.xBestIndex malfunction",pSrc->pTab->zName);
      testcase( pIdxInfo->needToFreeIdxStr );
      return SQLITE_ERROR;
    }
  }
  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;
  }
  rc = whereLoopInsert(pBuilder, pNew);
  if( pNew->u.vtab.needFree ){
    sqlite3_free(pNew->u.vtab.idxStr);
    pNew->u.vtab.needFree = 0;
  }
  WHERETRACE(0xffff, ("  bIn=%d prereqIn=%04llx prereqOut=%04llx\n",
                      *pbIn, (sqlite3_uint64)mPrereq,
                      (sqlite3_uint64)(pNew->prereq & ~mPrereq)));

  return rc;
}

/*
** If this function is invoked from within an xBestIndex() callback, it
** returns a pointer to a buffer containing the name of the collation
** sequence associated with element iCons of the sqlite3_index_info.aConstraint
** array. Or, if iCons is out of range or there is no active xBestIndex
** call, return NULL.
*/
const char *sqlite3_vtab_collation(sqlite3_index_info *pIdxInfo, int iCons){
  HiddenIndexInfo *pHidden = (HiddenIndexInfo*)&pIdxInfo[1];
  const char *zRet = 0;
  if( iCons>=0 && iCons<pIdxInfo->nConstraint ){
    CollSeq *pC = 0;
    int iTerm = pIdxInfo->aConstraint[iCons].iTermOffset;
    Expr *pX = pHidden->pWC->a[iTerm].pExpr;
    if( pX->pLeft ){
      pC = sqlite3ExprCompareCollSeq(pHidden->pParse, pX);
    }
    zRet = (pC ? pC->zName : sqlite3StrBINARY);
  }
  return zRet;
}

/*
** 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 mPrereq and
** mUnusable are set to 0. Otherwise, mPrereq 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 mPrereq corresponds to (t1, t2) and mUnusable to (t5, t6).
**
** All the tables in mPrereq must be scanned before the current virtual 
** table. So any terms for which all prerequisites are satisfied by 
** mPrereq 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 mPrereq,             /* Tables that must be scanned before this one */
  Bitmask mUnusable            /* Tables that must be scanned after this one */
){
  int rc = SQLITE_OK;          /* Return code */
  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 */
  sqlite3_index_info *p;       /* Object to pass to xBestIndex() */
  int nConstraint;             /* Number of constraints in p */
  int bIn;                     /* True if plan uses IN(...) operator */
  WhereLoop *pNew;
  Bitmask mBest;               /* Tables used by best possible plan */
  u16 mNoOmit;

  assert( (mPrereq & mUnusable)==0 );
  pWInfo = pBuilder->pWInfo;
  pParse = pWInfo->pParse;
  pWC = pBuilder->pWC;
  pNew = pBuilder->pNew;
  pSrc = &pWInfo->pTabList->a[pNew->iTab];
  assert( IsVirtual(pSrc->pTab) );
  p = allocateIndexInfo(pParse, pWC, mUnusable, pSrc, pBuilder->pOrderBy, 
      &mNoOmit);
  if( p==0 ) return SQLITE_NOMEM_BKPT;
  pNew->rSetup = 0;
  pNew->wsFlags = WHERE_VIRTUALTABLE;
  pNew->nLTerm = 0;
  pNew->u.vtab.needFree = 0;
  nConstraint = p->nConstraint;
  if( whereLoopResize(pParse->db, pNew, nConstraint) ){
    sqlite3DbFree(pParse->db, p);
    return SQLITE_NOMEM_BKPT;
  }

  /* First call xBestIndex() with all constraints usable. */
  WHERETRACE(0x800, ("BEGIN %s.addVirtual()\n", pSrc->pTab->zName));
  WHERETRACE(0x40, ("  VirtualOne: all usable\n"));
  rc = whereLoopAddVirtualOne(pBuilder, mPrereq, ALLBITS, 0, p, mNoOmit, &bIn);

  /* If the call to xBestIndex() with all terms enabled produced a plan
  ** that does not require any source tables (IOW: a plan with mBest==0)
  ** and does not use an IN(...) operator, then there is no point in making 
  ** any further calls to xBestIndex() since they will all return the same
  ** result (if the xBestIndex() implementation is sane). */
  if( rc==SQLITE_OK && ((mBest = (pNew->prereq & ~mPrereq))!=0 || bIn) ){
    int seenZero = 0;             /* True if a plan with no prereqs seen */
    int seenZeroNoIN = 0;         /* Plan with no prereqs and no IN(...) seen */
    Bitmask mPrev = 0;
    Bitmask mBestNoIn = 0;

    /* If the plan produced by the earlier call uses an IN(...) term, call
    ** xBestIndex again, this time with IN(...) terms disabled. */
    if( bIn ){
      WHERETRACE(0x40, ("  VirtualOne: all usable w/o IN\n"));
      rc = whereLoopAddVirtualOne(
          pBuilder, mPrereq, ALLBITS, WO_IN, p, mNoOmit, &bIn);
      assert( bIn==0 );
      mBestNoIn = pNew->prereq & ~mPrereq;
      if( mBestNoIn==0 ){
        seenZero = 1;
        seenZeroNoIN = 1;
      }
    }

    /* Call xBestIndex once for each distinct value of (prereqRight & ~mPrereq) 
    ** in the set of terms that apply to the current virtual table.  */
    while( rc==SQLITE_OK ){
      int i;
      Bitmask mNext = ALLBITS;
      assert( mNext>0 );
      for(i=0; i<nConstraint; i++){
        Bitmask mThis = (
            pWC->a[p->aConstraint[i].iTermOffset].prereqRight & ~mPrereq
        );
        if( mThis>mPrev && mThis<mNext ) mNext = mThis;
      }
      mPrev = mNext;
      if( mNext==ALLBITS ) break;
      if( mNext==mBest || mNext==mBestNoIn ) continue;
      WHERETRACE(0x40, ("  VirtualOne: mPrev=%04llx mNext=%04llx\n",
                       (sqlite3_uint64)mPrev, (sqlite3_uint64)mNext));
      rc = whereLoopAddVirtualOne(
          pBuilder, mPrereq, mNext|mPrereq, 0, p, mNoOmit, &bIn);
      if( pNew->prereq==mPrereq ){
        seenZero = 1;
        if( bIn==0 ) seenZeroNoIN = 1;
      }
    }

    /* If the calls to xBestIndex() in the above loop did not find a plan
    ** that requires no source tables at all (i.e. one guaranteed to be
    ** usable), make a call here with all source tables disabled */
    if( rc==SQLITE_OK && seenZero==0 ){
      WHERETRACE(0x40, ("  VirtualOne: all disabled\n"));
      rc = whereLoopAddVirtualOne(
          pBuilder, mPrereq, mPrereq, 0, p, mNoOmit, &bIn);
      if( bIn==0 ) seenZeroNoIN = 1;
    }

    /* If the calls to xBestIndex() have so far failed to find a plan
    ** that requires no source tables at all and does not use an IN(...)
    ** operator, make a final call to obtain one here.  */
    if( rc==SQLITE_OK && seenZeroNoIN==0 ){
      WHERETRACE(0x40, ("  VirtualOne: all disabled and w/o IN\n"));
      rc = whereLoopAddVirtualOne(
          pBuilder, mPrereq, mPrereq, WO_IN, p, mNoOmit, &bIn);
    }
  }

  if( p->needToFreeIdxStr ) sqlite3_free(p->idxStr);
  sqlite3DbFreeNN(pParse->db, p);
  WHERETRACE(0x800, ("END %s.addVirtual(), rc=%d\n", pSrc->pTab->zName, rc));
  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 mPrereq, 
  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 ){
          sqlite3WhereClausePrint(sSubBuild.pWC);
        }
#endif
#ifndef SQLITE_OMIT_VIRTUALTABLE
        if( IsVirtual(pItem->pTab) ){
          rc = whereLoopAddVirtual(&sSubBuild, mPrereq, mUnusable);
        }else
#endif
        {
          rc = whereLoopAddBtree(&sSubBuild, mPrereq);
        }
        if( rc==SQLITE_OK ){
          rc = whereLoopAddOr(&sSubBuild, mPrereq, mUnusable);
        }
        assert( rc==SQLITE_OK || rc==SQLITE_DONE || sCur.n==0 );
        testcase( rc==SQLITE_DONE );
        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 mPrereq = 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;

  /* Loop over the tables in the join, from left to right */
  pNew = pBuilder->pNew;
  whereLoopInit(pNew);
  pBuilder->iPlanLimit = SQLITE_QUERY_PLANNER_LIMIT;
  for(iTab=0, pItem=pTabList->a; pItem<pEnd; iTab++, pItem++){
    Bitmask mUnusable = 0;
    pNew->iTab = iTab;
    pBuilder->iPlanLimit += SQLITE_QUERY_PLANNER_LIMIT_INCR;
    pNew->maskSelf = sqlite3WhereGetMask(&pWInfo->sMaskSet, pItem->iCursor);
    if( (pItem->fg.jointype & (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.  */
      mPrereq = mPrior;
    }else{
      mPrereq = 0;
    }
#ifndef SQLITE_OMIT_VIRTUALTABLE
    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, mPrereq, mUnusable);
    }else
#endif /* SQLITE_OMIT_VIRTUALTABLE */
    {
      rc = whereLoopAddBtree(pBuilder, mPrereq);
    }
    if( rc==SQLITE_OK && pBuilder->pWC->hasOr ){
      rc = whereLoopAddOr(pBuilder, mPrereq, mUnusable);
    }
    mPrior |= pNew->maskSelf;
    if( rc || db->mallocFailed ){
      if( rc==SQLITE_DONE ){
        /* We hit the query planner search limit set by iPlanLimit */
        sqlite3_log(SQLITE_WARNING, "abbreviated query algorithm search");
        rc = SQLITE_OK;
      }else{
        break;
      }
    }
  }

  whereLoopClear(db, pNew);
  return rc;
}

/*
** Examine a WherePath (with the addition of the extra WhereLoop of the 6th
** 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,       /* WHERE_GROUPBY or _DISTINCTBY or _ORDERBY_LIMIT */
  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 eqOpMask;         /* Allowed equality operators */
  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;
  eqOpMask = WO_EQ | WO_IS | WO_ISNULL;
  if( wctrlFlags & (WHERE_ORDERBY_LIMIT|WHERE_ORDERBY_MAX|WHERE_ORDERBY_MIN) ){
    eqOpMask |= WO_IN;
  }
  for(iLoop=0; isOrderDistinct && obSat<obDone && iLoop<=nLoop; iLoop++){
    if( iLoop>0 ) ready |= pLoop->maskSelf;
    if( iLoop<nLoop ){
      pLoop = pPath->aLoop[iLoop];
      if( wctrlFlags & WHERE_ORDERBY_LIMIT ) continue;
    }else{
      pLoop = pLast;
    }
    if( pLoop->wsFlags & WHERE_VIRTUALTABLE ){
      if( pLoop->u.vtab.isOrdered && (wctrlFlags & WHERE_DISTINCTBY)==0 ){
        obSat = obDone;
      }
      break;
    }else if( wctrlFlags & WHERE_DISTINCTBY ){
      pLoop->u.btree.nDistinctCol = 0;
    }
    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 = sqlite3ExprSkipCollateAndLikely(pOrderBy->a[i].pExpr);
      if( pOBExpr->op!=TK_COLUMN ) continue;
      if( pOBExpr->iTable!=iCur ) continue;
      pTerm = sqlite3WhereFindTerm(&pWInfo->sWC, iCur, pOBExpr->iColumn,
                       ~ready, eqOpMask, 0);
      if( pTerm==0 ) continue;
      if( pTerm->eOperator==WO_IN ){
        /* IN terms are only valid for sorting in the ORDER BY LIMIT 
        ** optimization, and then only if they are actually used
        ** by the query plan */
        assert( wctrlFlags & 
               (WHERE_ORDERBY_LIMIT|WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX) );
        for(j=0; j<pLoop->nLTerm && pTerm!=pLoop->aLTerm[j]; j++){}
        if( j>=pLoop->nLTerm ) continue;
      }
      if( (pTerm->eOperator&(WO_EQ|WO_IS))!=0 && pOBExpr->iColumn>=0 ){
        Parse *pParse = pWInfo->pParse;
        CollSeq *pColl1 = sqlite3ExprNNCollSeq(pParse, pOrderBy->a[i].pExpr);
        CollSeq *pColl2 = sqlite3ExprCompareCollSeq(pParse, pTerm->pExpr);
        assert( pColl1 );
        if( pColl2==0 || sqlite3StrICmp(pColl1->zName, pColl2->zName) ){
          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)
                          && (pLoop->wsFlags & WHERE_SKIPSCAN)==0;
      }

      /* 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 = 1; /* True to run the ORDER BY search loop */

        assert( j>=pLoop->u.btree.nEq 
            || (pLoop->aLTerm[j]==0)==(j<pLoop->nSkip)
        );
        if( j<pLoop->u.btree.nEq && j>=pLoop->nSkip ){
          u16 eOp = pLoop->aLTerm[j]->eOperator;

          /* Skip over == and IS and ISNULL terms.  (Also skip IN terms when
          ** doing WHERE_ORDERBY_LIMIT processing).  Except, IS and ISNULL
          ** terms imply that the index is not UNIQUE NOT NULL in which case
          ** the loop need to be marked as not order-distinct because it can
          ** have repeated NULL rows.
          **
          ** If the current term is a column of an ((?,?) IN (SELECT...)) 
          ** expression for which the SELECT returns more than one column,
          ** check that it is the only column used by this loop. Otherwise,
          ** if it is one of two or more, none of the columns can be
          ** considered to match an ORDER BY term.
          */
          if( (eOp & eqOpMask)!=0 ){
            if( eOp & (WO_ISNULL|WO_IS) ){
              testcase( eOp & WO_ISNULL );
              testcase( eOp & WO_IS );
              testcase( isOrderDistinct );
              isOrderDistinct = 0;
            }
            continue;  
          }else if( ALWAYS(eOp & WO_IN) ){
            /* ALWAYS() justification: eOp is an equality operator due to the
            ** j<pLoop->u.btree.nEq constraint above.  Any equality other
            ** than WO_IN is captured by the previous "if".  So this one
            ** always has to be WO_IN. */
            Expr *pX = pLoop->aLTerm[j]->pExpr;
            for(i=j+1; i<pLoop->u.btree.nEq; i++){
              if( pLoop->aLTerm[i]->pExpr==pX ){
                assert( (pLoop->aLTerm[i]->eOperator & WO_IN) );
                bOnce = 0;
                break;
              }
            }
          }
        }

        /* 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] & KEYINFO_ORDER_DESC;
          if( iColumn==pIndex->pTable->iPKey ) iColumn = XN_ROWID;
        }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 
        */
        isMatch = 0;
        for(i=0; bOnce && i<nOrderBy; i++){
          if( MASKBIT(i) & obSat ) continue;
          pOBExpr = sqlite3ExprSkipCollateAndLikely(pOrderBy->a[i].pExpr);
          testcase( wctrlFlags & WHERE_GROUPBY );
          testcase( wctrlFlags & WHERE_DISTINCTBY );
          if( (wctrlFlags & (WHERE_GROUPBY|WHERE_DISTINCTBY))==0 ) bOnce = 0;
          if( iColumn>=XN_ROWID ){
            if( pOBExpr->op!=TK_COLUMN ) continue;
            if( pOBExpr->iTable!=iCur ) continue;
            if( pOBExpr->iColumn!=iColumn ) continue;
          }else{
            Expr *pIdxExpr = pIndex->aColExpr->a[j].pExpr;
            if( sqlite3ExprCompareSkip(pOBExpr, pIdxExpr, iCur) ){
              continue;
            }
          }
          if( iColumn!=XN_ROWID ){
            pColl = sqlite3ExprNNCollSeq(pWInfo->pParse, pOrderBy->a[i].pExpr);
            if( sqlite3StrICmp(pColl->zName, pIndex->azColl[j])!=0 ) continue;
          }
          if( wctrlFlags & WHERE_DISTINCTBY ){
            pLoop->u.btree.nDistinctCol = j+1;
          }
          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].sortFlags&KEYINFO_ORDER_DESC) ){
              isMatch = 0;
            }
          }else{
            rev = revIdx ^ (pOrderBy->a[i].sortFlags & KEYINFO_ORDER_DESC);
            if( rev ) *pRevMask |= MASKBIT(iLoop);
            revSet = 1;
          }
        }
        if( isMatch && (pOrderBy->a[i].sortFlags & KEYINFO_ORDER_BIGNULL) ){
          if( j==pLoop->u.btree.nEq ){
            pLoop->wsFlags |= WHERE_BIGNULL_SORT;
          }else{
            isMatch = 0;
          }
        }
        if( isMatch ){
          if( iColumn==XN_ROWID ){
            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 + rScale + 16;

  /* Multiple by log(M) where M is the number of output rows.
  ** Use the LIMIT for M if it is smaller */
  if( (pWInfo->wctrlFlags & WHERE_USE_LIMIT)!=0 && pWInfo->iLimit<nRow ){
    nRow = pWInfo->iLimit;
  }
  rSortCost += estLog(nRow);
  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 = sqlite3DbMallocRawNN(db, nSpace);
  if( pSpace==0 ) return SQLITE_NOMEM_BKPT;
  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;
        if( (pWLoop->wsFlags & WHERE_AUTO_INDEX)!=0 && pFrom->nRow<3 ){
          /* Do not use an automatic index if the this loop is expected
          ** to run less than 1.25 times.  It is tempting to also exclude
          ** automatic index usage on an outer loop, but sometimes an automatic
          ** index is useful in the outer loop of a correlated subquery. */
          assert( 10==sqlite3LogEst(2) );
          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
            );
          }
          /* TUNING:  Add a small extra penalty (5) to sorting as an
          ** extra encouragment to the query planner to select a plan
          ** where the rows emerge in the correct order without any sorting
          ** required. */
          rCost = sqlite3LogEstAdd(rUnsorted, aSortCost[isOrdered]) + 5;

          WHERETRACE(0x002,
              ("---- sort cost=%-3d (%d/%d) increases cost %3d to %-3d\n",
               aSortCost[isOrdered], (nOrderBy-isOrdered), nOrderBy, 
               rUnsorted, rCost));
        }else{
          rCost = rUnsorted;
          rUnsorted -= 2;  /* TUNING:  Slight bias in favor of no-sort plans */
        }

        /* 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,%3d order=%c\n",
                  wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,
                  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,%3d order=%c\n",
                wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,
                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 same isOrdered setting as the
          ** candidate path.  Check to see if the candidate should replace
          ** pTo or if the candidate should be skipped.
          ** 
          ** The conditional is an expanded vector comparison equivalent to:
          **   (pTo->rCost,pTo->nRow,pTo->rUnsorted) <= (rCost,nOut,rUnsorted)
          */
          if( pTo->rCost<rCost 
           || (pTo->rCost==rCost
               && (pTo->nRow<nOut
                   || (pTo->nRow==nOut && pTo->rUnsorted<=rUnsorted)
                  )
              )
          ){
#ifdef WHERETRACE_ENABLED /* 0x4 */
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf(
                  "Skip   %s cost=%-3d,%3d,%3d order=%c",
                  wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,
                  isOrdered>=0 ? isOrdered+'0' : '?');
              sqlite3DebugPrintf("   vs %s cost=%-3d,%3d,%3d order=%c\n",
                  wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
                  pTo->rUnsorted, 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,%3d order=%c",
                wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,
                isOrdered>=0 ? isOrdered+'0' : '?');
            sqlite3DebugPrintf("  was %s cost=%-3d,%3d,%3d order=%c\n",
                wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
                pTo->rUnsorted, 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");
    sqlite3DbFreeNN(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;
    }
  }
  pWInfo->bOrderedInnerLoop = 0;
  if( pWInfo->pOrderBy ){
    if( pWInfo->wctrlFlags & WHERE_DISTINCTBY ){
      if( pFrom->isOrdered==pWInfo->pOrderBy->nExpr ){
        pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;
      }
    }else{
      pWInfo->nOBSat = pFrom->isOrdered;
      pWInfo->revMask = pFrom->revLoop;
      if( pWInfo->nOBSat<=0 ){
        pWInfo->nOBSat = 0;
        if( nLoop>0 ){
          u32 wsFlags = pFrom->aLoop[nLoop-1]->wsFlags;
          if( (wsFlags & WHERE_ONEROW)==0 
           && (wsFlags&(WHERE_IPK|WHERE_COLUMN_IN))!=(WHERE_IPK|WHERE_COLUMN_IN)
          ){
            Bitmask m = 0;
            int rc = wherePathSatisfiesOrderBy(pWInfo, pWInfo->pOrderBy, pFrom,
                      WHERE_ORDERBY_LIMIT, nLoop-1, pFrom->aLoop[nLoop-1], &m);
            testcase( wsFlags & WHERE_IPK );
            testcase( wsFlags & WHERE_COLUMN_IN );
            if( rc==pWInfo->pOrderBy->nExpr ){
              pWInfo->bOrderedInnerLoop = 1;
              pWInfo->revMask = m;
            }
          }
        }
      }else if( nLoop
            && pWInfo->nOBSat==1
            && (pWInfo->wctrlFlags & (WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX))!=0
            ){
        pWInfo->bOrderedInnerLoop = 1;
      }
    }
    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 */
  sqlite3DbFreeNN(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_OR_SUBCLAUSE ) 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 & pIdx->colNotIdxed)==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;
    assert( pWInfo->sMaskSet.n==1 && iCur==pWInfo->sMaskSet.ix[0] );
    pLoop->maskSelf = 1; /* 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;
}

/*
** Helper function for exprIsDeterministic().
*/
static int exprNodeIsDeterministic(Walker *pWalker, Expr *pExpr){
  if( pExpr->op==TK_FUNCTION && ExprHasProperty(pExpr, EP_ConstFunc)==0 ){
    pWalker->eCode = 0;
    return WRC_Abort;
  }
  return WRC_Continue;
}

/*
** Return true if the expression contains no non-deterministic SQL 
** functions. Do not consider non-deterministic SQL functions that are 
** part of sub-select statements.
*/
static int exprIsDeterministic(Expr *p){
  Walker w;
  memset(&w, 0, sizeof(w));
  w.eCode = 1;
  w.xExprCallback = exprNodeIsDeterministic;
  w.xSelectCallback = sqlite3SelectWalkFail;
  sqlite3WalkExpr(&w, p);
  return w.eCode;
}

  
#ifdef WHERETRACE_ENABLED
/*
** Display all WhereLoops in pWInfo
*/
static void showAllWhereLoops(WhereInfo *pWInfo, WhereClause *pWC){
  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)-1)];
      sqlite3WhereLoopPrint(p, pWC);
    }
  }
}
# define WHERETRACE_ALL_LOOPS(W,C) showAllWhereLoops(W,C)
#else
# define WHERETRACE_ALL_LOOPS(W,C)
#endif

/*
** 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_OR_SUBCLAUSE 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,   /* Query result set.  Req'd for DISTINCT */
  u16 wctrlFlags,         /* The WHERE_* flags defined in sqliteInt.h */
  int iAuxArg             /* If WHERE_OR_SUBCLAUSE is set, index cursor number
                          ** If WHERE_USE_LIMIT, then the limit amount */
){
  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 */
  u8 bFordelete = 0;         /* OPFLAG_FORDELETE or zero, as appropriate */

  assert( (wctrlFlags & WHERE_ONEPASS_MULTIROW)==0 || (
        (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 
     && (wctrlFlags & WHERE_OR_SUBCLAUSE)==0 
  ));

  /* Only one of WHERE_OR_SUBCLAUSE or WHERE_USE_LIMIT */
  assert( (wctrlFlags & WHERE_OR_SUBCLAUSE)==0
            || (wctrlFlags & WHERE_USE_LIMIT)==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_OR_SUBCLAUSE 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_OR_SUBCLAUSE) ? 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 = sqlite3DbMallocRawNN(db, nByteWInfo + sizeof(WhereLoop));
  if( db->mallocFailed ){
    sqlite3DbFree(db, pWInfo);
    pWInfo = 0;
    goto whereBeginError;
  }
  pWInfo->pParse = pParse;
  pWInfo->pTabList = pTabList;
  pWInfo->pOrderBy = pOrderBy;
  pWInfo->pWhere = pWhere;
  pWInfo->pResultSet = pResultSet;
  pWInfo->aiCurOnePass[0] = pWInfo->aiCurOnePass[1] = -1;
  pWInfo->nLevel = nTabList;
  pWInfo->iBreak = pWInfo->iContinue = sqlite3VdbeMakeLabel(pParse);
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->iLimit = iAuxArg;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  memset(&pWInfo->nOBSat, 0, 
         offsetof(WhereInfo,sWC) - offsetof(WhereInfo,nOBSat));
  memset(&pWInfo->a[0], 0, sizeof(WhereLoop)+nTabList*sizeof(WhereLevel));
  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: No FROM clause
  */
  if( nTabList==0 ){
    if( pOrderBy ) pWInfo->nOBSat = pOrderBy->nExpr;
    if( wctrlFlags & WHERE_WANT_DISTINCT ){
      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
    }
    ExplainQueryPlan((pParse, 0, "SCAN CONSTANT ROW"));
  }else{
    /* 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_OR_SUBCLAUSE flag is set.
    */
    ii = 0;
    do{
      createMask(pMaskSet, pTabList->a[ii].iCursor);
      sqlite3WhereTabFuncArgs(pParse, &pTabList->a[ii], &pWInfo->sWC);
    }while( (++ii)<pTabList->nSrc );
  #ifdef SQLITE_DEBUG
    {
      Bitmask mx = 0;
      for(ii=0; ii<pTabList->nSrc; ii++){
        Bitmask m = sqlite3WhereGetMask(pMaskSet, pTabList->a[ii].iCursor);
        assert( m>=mx );
        mx = m;
      }
    }
  #endif
  }
  
  /* Analyze all of the subexpressions. */
  sqlite3WhereExprAnalyze(pTabList, &pWInfo->sWC);
  if( db->mallocFailed ) goto whereBeginError;

  /* Special case: WHERE terms that do not refer to any tables in the join
  ** (constant expressions). Evaluate each such term, and jump over all the
  ** generated code if the result is not true.  
  **
  ** Do not do this if the expression contains non-deterministic functions
  ** that are not within a sub-select. This is not strictly required, but
  ** preserves SQLite's legacy behaviour in the following two cases:
  **
  **   FROM ... WHERE random()>0;           -- eval random() once per row
  **   FROM ... WHERE (SELECT random())>0;  -- eval random() once overall
  */
  for(ii=0; ii<sWLB.pWC->nTerm; ii++){
    WhereTerm *pT = &sWLB.pWC->a[ii];
    if( pT->wtFlags & TERM_VIRTUAL ) continue;
    if( pT->prereqAll==0 && (nTabList==0 || exprIsDeterministic(pT->pExpr)) ){
      sqlite3ExprIfFalse(pParse, pT->pExpr, pWInfo->iBreak, SQLITE_JUMPIFNULL);
      pT->wtFlags |= TERM_CODED;
    }
  }

  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 */
#if defined(WHERETRACE_ENABLED)
  if( sqlite3WhereTrace & 0xffff ){
    sqlite3DebugPrintf("*** Optimizer Start *** (wctrlFlags: 0x%x",wctrlFlags);
    if( wctrlFlags & WHERE_USE_LIMIT ){
      sqlite3DebugPrintf(", limit: %d", iAuxArg);
    }
    sqlite3DebugPrintf(")\n");
    if( sqlite3WhereTrace & 0x100 ){
      Select sSelect;
      memset(&sSelect, 0, sizeof(sSelect));
      sSelect.selFlags = SF_WhereBegin;
      sSelect.pSrc = pTabList;
      sSelect.pWhere = pWhere;
      sSelect.pOrderBy = pOrderBy;
      sSelect.pEList = pResultSet;
      sqlite3TreeViewSelect(0, &sSelect, 0);
    }
  }
  if( sqlite3WhereTrace & 0x100 ){ /* Display all terms of the WHERE clause */
    sqlite3DebugPrintf("---- WHERE clause at start of analysis:\n");
    sqlite3WhereClausePrint(sWLB.pWC);
  }
#endif

  if( nTabList!=1 || whereShortCut(&sWLB)==0 ){
    rc = whereLoopAddAll(&sWLB);
    if( rc ) goto whereBeginError;

#ifdef SQLITE_ENABLE_STAT4
    /* If one or more WhereTerm.truthProb values were used in estimating
    ** loop parameters, but then those truthProb values were subsequently
    ** changed based on STAT4 information while computing subsequent loops,
    ** then we need to rerun the whole loop building process so that all
    ** loops will be built using the revised truthProb values. */
    if( sWLB.bldFlags2 & SQLITE_BLDF2_2NDPASS ){
      WHERETRACE_ALL_LOOPS(pWInfo, sWLB.pWC);
      WHERETRACE(0xffff, 
           ("**** Redo all loop computations due to"
            " TERM_HIGHTRUTH changes ****\n"));
      while( pWInfo->pLoops ){
        WhereLoop *p = pWInfo->pLoops;
        pWInfo->pLoops = p->pNextLoop;
        whereLoopDelete(db, p);
      }
      rc = whereLoopAddAll(&sWLB);
      if( rc ) goto whereBeginError;
    }
#endif
    WHERETRACE_ALL_LOOPS(pWInfo, sWLB.pWC);
  
    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 = ALLBITS;
  }
  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++){
      sqlite3WhereLoopPrint(pWInfo->a[ii].pWLoop, sWLB.pWC);
    }
  }
#endif

  /* Attempt to omit tables from the join that do not affect the result.
  ** For a table to not affect the result, the following must be true:
  **
  **   1) The query must not be an aggregate.
  **   2) The table must be the RHS of a LEFT JOIN.
  **   3) Either the query must be DISTINCT, or else the ON or USING clause
  **      must contain a constraint that limits the scan of the table to 
  **      at most a single row.
  **   4) The table must not be referenced by any part of the query apart
  **      from its own USING or ON clause.
  **
  ** For example, given:
  **
  **     CREATE TABLE t1(ipk INTEGER PRIMARY KEY, v1);
  **     CREATE TABLE t2(ipk INTEGER PRIMARY KEY, v2);
  **     CREATE TABLE t3(ipk INTEGER PRIMARY KEY, v3);
  **
  ** then table t2 can be omitted from the following:
  **
  **     SELECT v1, v3 FROM t1 
  **       LEFT JOIN t2 ON (t1.ipk=t2.ipk)
  **       LEFT JOIN t3 ON (t1.ipk=t3.ipk)
  **
  ** or from:
  **
  **     SELECT DISTINCT v1, v3 FROM t1 
  **       LEFT JOIN t2
  **       LEFT JOIN t3 ON (t1.ipk=t3.ipk)
  */
  notReady = ~(Bitmask)0;
  if( pWInfo->nLevel>=2
   && pResultSet!=0               /* guarantees condition (1) above */
   && OptimizationEnabled(db, SQLITE_OmitNoopJoin)
  ){
    int i;
    Bitmask tabUsed = sqlite3WhereExprListUsage(pMaskSet, pResultSet);
    if( sWLB.pOrderBy ){
      tabUsed |= sqlite3WhereExprListUsage(pMaskSet, sWLB.pOrderBy);
    }
    for(i=pWInfo->nLevel-1; i>=1; i--){
      WhereTerm *pTerm, *pEnd;
      struct SrcList_item *pItem;
      pLoop = pWInfo->a[i].pWLoop;
      pItem = &pWInfo->pTabList->a[pLoop->iTab];
      if( (pItem->fg.jointype & JT_LEFT)==0 ) continue;
      if( (wctrlFlags & WHERE_WANT_DISTINCT)==0
       && (pLoop->wsFlags & WHERE_ONEROW)==0
      ){
        continue;
      }
      if( (tabUsed & pLoop->maskSelf)!=0 ) continue;
      pEnd = sWLB.pWC->a + sWLB.pWC->nTerm;
      for(pTerm=sWLB.pWC->a; pTerm<pEnd; pTerm++){
        if( (pTerm->prereqAll & pLoop->maskSelf)!=0 ){
          if( !ExprHasProperty(pTerm->pExpr, EP_FromJoin)
           || pTerm->pExpr->iRightJoinTable!=pItem->iCursor
          ){
            break;
          }
        }
      }
      if( pTerm<pEnd ) continue;
      WHERETRACE(0xffff, ("-> drop loop %c not used\n", pLoop->cId));
      notReady &= ~pLoop->maskSelf;
      for(pTerm=sWLB.pWC->a; pTerm<pEnd; pTerm++){
        if( (pTerm->prereqAll & pLoop->maskSelf)!=0 ){
          pTerm->wtFlags |= TERM_CODED;
        }
      }
      if( i!=pWInfo->nLevel-1 ){
        int nByte = (pWInfo->nLevel-1-i) * sizeof(WhereLevel);
        memmove(&pWInfo->a[i], &pWInfo->a[i+1], nByte);
      }
      pWInfo->nLevel--;
      nTabList--;
    }
  }
#if defined(WHERETRACE_ENABLED)
  if( sqlite3WhereTrace & 0x100 ){ /* Display all terms of the WHERE clause */
    sqlite3DebugPrintf("---- WHERE clause at end of analysis:\n");
    sqlite3WhereClausePrint(sWLB.pWC);
  }
  WHERETRACE(0xffff,("*** Optimizer Finished ***\n"));
#endif
  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.
  **
  ** A one-pass approach can be used if the caller has requested one
  ** and either (a) the scan visits at most one row or (b) each
  ** of the following are true:
  **
  **   * the caller has indicated that a one-pass approach can be used
  **     with multiple rows (by setting WHERE_ONEPASS_MULTIROW), and
  **   * the table is not a virtual table, and
  **   * either the scan does not use the OR optimization or the caller
  **     is a DELETE operation (WHERE_DUPLICATES_OK is only specified
  **     for DELETE).
  **
  ** The last qualification is because an UPDATE statement uses
  ** WhereInfo.aiCurOnePass[1] to determine whether or not it really can
  ** use a one-pass approach, and this is not set accurately for scans
  ** that use the OR optimization.
  */
  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;
    assert( !(wsFlags & WHERE_VIRTUALTABLE) || IsVirtual(pTabList->a[0].pTab) );
    if( bOnerow || (
        0!=(wctrlFlags & WHERE_ONEPASS_MULTIROW)
     && !IsVirtual(pTabList->a[0].pTab)
     && (0==(wsFlags & WHERE_MULTI_OR) || (wctrlFlags & WHERE_DUPLICATES_OK))
    )){
      pWInfo->eOnePass = bOnerow ? ONEPASS_SINGLE : ONEPASS_MULTI;
      if( HasRowid(pTabList->a[0].pTab) && (wsFlags & WHERE_IDX_ONLY) ){
        if( wctrlFlags & WHERE_ONEPASS_MULTIROW ){
          bFordelete = OPFLAG_FORDELETE;
        }
        pWInfo->a[0].pWLoop->wsFlags = (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_OR_SUBCLAUSE)==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
       && (pTab->tabFlags & (TF_HasGenerated|TF_WithoutRowid))==0
      ){
        /* If we know that only a prefix of the record will be used,
        ** it is advantageous to reduce the "column count" field in
        ** the P4 operand of the OP_OpenRead/Write opcode. */
        Bitmask b = pTabItem->colUsed;
        int n = 0;
        for(; b; b=b>>1, n++){}
        sqlite3VdbeChangeP4(v, -1, SQLITE_INT_TO_PTR(n), P4_INT32);
        assert( n<=pTab->nCol );
      }
#ifdef SQLITE_ENABLE_CURSOR_HINTS
      if( pLoop->u.btree.pIndex!=0 ){
        sqlite3VdbeChangeP5(v, OPFLAG_SEEKEQ|bFordelete);
      }else
#endif
      {
        sqlite3VdbeChangeP5(v, bFordelete);
      }
#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;
      /* iAuxArg is always set to a positive value if ONEPASS is possible */
      assert( iAuxArg!=0 || (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0 );
      if( !HasRowid(pTab) && IsPrimaryKeyIndex(pIx)
       && (wctrlFlags & WHERE_OR_SUBCLAUSE)!=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 = iAuxArg;
        assert( wctrlFlags & WHERE_ONEPASS_DESIRED );
        while( ALWAYS(pJ) && pJ!=pIx ){
          iIndexCur++;
          pJ = pJ->pNext;
        }
        op = OP_OpenWrite;
        pWInfo->aiCurOnePass[1] = iIndexCur;
      }else if( iAuxArg && (wctrlFlags & WHERE_OR_SUBCLAUSE)!=0 ){
        iIndexCur = iAuxArg;
        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
         && (pLoop->wsFlags & WHERE_BIGNULL_SORT)==0
         && (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)==0
         && pWInfo->eDistinct!=WHERE_DISTINCT_ORDERED
        ){
          sqlite3VdbeChangeP5(v, OPFLAG_SEEKEQ);
        }
        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.
  */
  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, wctrlFlags
    );
    pLevel->addrBody = sqlite3VdbeCurrentAddr(v);
    notReady = sqlite3WhereCodeOneLoopStart(pParse,v,pWInfo,ii,pLevel,notReady);
    pWInfo->iContinue = pLevel->addrCont;
    if( (wsFlags&WHERE_MULTI_OR)==0 && (wctrlFlags&WHERE_OR_SUBCLAUSE)==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;
}

/*
** Part of sqlite3WhereEnd() will rewrite opcodes to reference the
** index rather than the main table.  In SQLITE_DEBUG mode, we want
** to trace those changes if PRAGMA vdbe_addoptrace=on.  This routine
** does that.
*/
#ifndef SQLITE_DEBUG
# define OpcodeRewriteTrace(D,K,P) /* no-op */
#else
# define OpcodeRewriteTrace(D,K,P) sqlite3WhereOpcodeRewriteTrace(D,K,P)
  static void sqlite3WhereOpcodeRewriteTrace(
    sqlite3 *db,
    int pc,
    VdbeOp *pOp
  ){
    if( (db->flags & SQLITE_VdbeAddopTrace)==0 ) return;
    sqlite3VdbePrintOp(0, pc, pOp);
  }
#endif

/*
** 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"));
  for(i=pWInfo->nLevel-1; i>=0; i--){
    int addr;
    pLevel = &pWInfo->a[i];
    pLoop = pLevel->pWLoop;
    if( pLevel->op!=OP_Noop ){
#ifndef SQLITE_DISABLE_SKIPAHEAD_DISTINCT
      int addrSeek = 0;
      Index *pIdx;
      int n;
      if( pWInfo->eDistinct==WHERE_DISTINCT_ORDERED
       && i==pWInfo->nLevel-1  /* Ticket [ef9318757b152e3] 2017-10-21 */
       && (pLoop->wsFlags & WHERE_INDEXED)!=0
       && (pIdx = pLoop->u.btree.pIndex)->hasStat1
       && (n = pLoop->u.btree.nDistinctCol)>0
       && pIdx->aiRowLogEst[n]>=36
      ){
        int r1 = pParse->nMem+1;
        int j, op;
        for(j=0; j<n; j++){
          sqlite3VdbeAddOp3(v, OP_Column, pLevel->iIdxCur, j, r1+j);
        }
        pParse->nMem += n+1;
        op = pLevel->op==OP_Prev ? OP_SeekLT : OP_SeekGT;
        addrSeek = sqlite3VdbeAddOp4Int(v, op, pLevel->iIdxCur, 0, r1, n);
        VdbeCoverageIf(v, op==OP_SeekLT);
        VdbeCoverageIf(v, op==OP_SeekGT);
        sqlite3VdbeAddOp2(v, OP_Goto, 1, pLevel->p2);
      }
#endif /* SQLITE_DISABLE_SKIPAHEAD_DISTINCT */
      /* The common case: Advance to the next row */
      sqlite3VdbeResolveLabel(v, pLevel->addrCont);
      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( pLevel->regBignull ){
        sqlite3VdbeResolveLabel(v, pLevel->addrBignull);
        sqlite3VdbeAddOp2(v, OP_DecrJumpZero, pLevel->regBignull, pLevel->p2-1);
        VdbeCoverage(v);
      }
#ifndef SQLITE_DISABLE_SKIPAHEAD_DISTINCT
      if( addrSeek ) sqlite3VdbeJumpHere(v, addrSeek);
#endif
    }else{
      sqlite3VdbeResolveLabel(v, pLevel->addrCont);
    }
    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);
        if( pIn->eEndLoopOp!=OP_Noop ){
          if( pIn->nPrefix ){
            assert( pLoop->wsFlags & WHERE_IN_EARLYOUT );
            if( pLevel->iLeftJoin ){
              /* For LEFT JOIN queries, cursor pIn->iCur may not have been
              ** opened yet. This occurs for WHERE clauses such as
              ** "a = ? AND b IN (...)", where the index is on (a, b). If
              ** the RHS of the (a=?) is NULL, then the "b IN (...)" may
              ** never have been coded, but the body of the loop run to
              ** return the null-row. So, if the cursor is not open yet,
              ** jump over the OP_Next or OP_Prev instruction about to
              ** be coded.  */
              sqlite3VdbeAddOp2(v, OP_IfNotOpen, pIn->iCur, 
                  sqlite3VdbeCurrentAddr(v) + 2 + 
                     ((pLoop->wsFlags & WHERE_VIRTUALTABLE)==0)
              );
              VdbeCoverage(v);
            }
            if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0 ){
              sqlite3VdbeAddOp4Int(v, OP_IfNoHope, pLevel->iIdxCur,
                  sqlite3VdbeCurrentAddr(v)+2,
                  pIn->iBase, pIn->nPrefix);
              VdbeCoverage(v);
            }
          }
          sqlite3VdbeAddOp2(v, pIn->eEndLoopOp, pIn->iCur, pIn->addrInTop);
          VdbeCoverage(v);
          VdbeCoverageIf(v, pIn->eEndLoopOp==OP_Prev);
          VdbeCoverageIf(v, pIn->eEndLoopOp==OP_Next);
        }
        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);
    }
#ifndef SQLITE_LIKE_DOESNT_MATCH_BLOBS
    if( pLevel->addrLikeRep ){
      sqlite3VdbeAddOp2(v, OP_DecrJumpZero, (int)(pLevel->iLikeRepCntr>>1),
                        pLevel->addrLikeRep);
      VdbeCoverage(v);
    }
#endif
    if( pLevel->iLeftJoin ){
      int ws = pLoop->wsFlags;
      addr = sqlite3VdbeAddOp1(v, OP_IfPos, pLevel->iLeftJoin); VdbeCoverage(v);
      assert( (ws & WHERE_IDX_ONLY)==0 || (ws & WHERE_INDEXED)!=0 );
      if( (ws & WHERE_IDX_ONLY)==0 ){
        assert( pLevel->iTabCur==pTabList->a[pLevel->iFrom].iCursor );
        sqlite3VdbeAddOp1(v, OP_NullRow, pLevel->iTabCur);
      }
      if( (ws & WHERE_INDEXED) 
       || ((ws & WHERE_MULTI_OR) && pLevel->u.pCovidx) 
      ){
        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 ){
      testcase( pParse->db->mallocFailed );
      translateColumnToCopy(pParse, pLevel->addrBody, pLevel->iTabCur,
                            pTabItem->regResult, 0);
      continue;
    }

#ifdef SQLITE_ENABLE_EARLY_CURSOR_CLOSE
    /* Close all of the cursors that were opened by sqlite3WhereBegin.
    ** Except, do not close cursors that will be reused by the OR optimization
    ** (WHERE_OR_SUBCLAUSE).  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_OR_SUBCLAUSE)==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);
      }
    }
#endif

    /* 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;
#ifdef SQLITE_DEBUG
      if( db->flags & SQLITE_VdbeAddopTrace ){
        printf("TRANSLATE opcodes in range %d..%d\n", k, last-1);
      }
#endif
      pOp = sqlite3VdbeGetOp(v, k);
      for(; k<last; k++, pOp++){
        if( pOp->p1!=pLevel->iTabCur ) continue;
        if( pOp->opcode==OP_Column
#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC
         || pOp->opcode==OP_Offset
#endif
        ){
          int x = pOp->p2;
          assert( pIdx->pTable==pTab );
          if( !HasRowid(pTab) ){
            Index *pPk = sqlite3PrimaryKeyIndex(pTab);
            x = pPk->aiColumn[x];
            assert( x>=0 );
          }else{
            testcase( x!=sqlite3StorageColumnToTable(pTab,x) );
            x = sqlite3StorageColumnToTable(pTab,x);
          }
          x = sqlite3TableColumnToIndex(pIdx, x);
          if( x>=0 ){
            pOp->p2 = x;
            pOp->p1 = pLevel->iIdxCur;
            OpcodeRewriteTrace(db, k, pOp);
          }
          assert( (pLoop->wsFlags & WHERE_IDX_ONLY)==0 || x>=0 
              || pWInfo->eOnePass );
        }else if( pOp->opcode==OP_Rowid ){
          pOp->p1 = pLevel->iIdxCur;
          pOp->opcode = OP_IdxRowid;
          OpcodeRewriteTrace(db, k, pOp);
        }else if( pOp->opcode==OP_IfNullRow ){
          pOp->p1 = pLevel->iIdxCur;
          OpcodeRewriteTrace(db, k, pOp);
        }
      }
#ifdef SQLITE_DEBUG
      if( db->flags & SQLITE_VdbeAddopTrace ) printf("TRANSLATE complete\n");
#endif
    }
  }

  /* Undo all Expr node modifications */
  while( pWInfo->pExprMods ){
    WhereExprMod *p = pWInfo->pExprMods;
    pWInfo->pExprMods = p->pNext;
    memcpy(p->pExpr, &p->orig, sizeof(p->orig));
    sqlite3DbFree(db, p);
  }

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