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);


      if( (idxCols & cMask)==0 ){
        Expr *pX = pTerm->pExpr;
        idxCols |= cMask;
        pIdx->aiColumn[n] = pTerm->u.leftColumn;
        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
        pIdx->azColl[n] = ALWAYS(pColl) ? pColl->zName : "BINARY";
        n++;
................................................................................
  Index *pIndex = pLoop->u.btree.pIndex;
  int nEq = pLoop->u.btree.nEq;
  int i, j;
  Column *aCol = pTab->aCol;
  int *aiColumn = pIndex->aiColumn;
  StrAccum txt;

  if( pIndex==0 ) return 0;
  if( nEq==0 && (pLoop->wsFlags & (WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))==0 ){
    return 0;
  }
  sqlite3StrAccumInit(&txt, 0, 0, SQLITE_MAX_LENGTH);
  txt.db = db;
  sqlite3StrAccumAppend(&txt, " (", 2);
  for(i=0; i<nEq; i++){
................................................................................
      zMsg = sqlite3MAppendf(db, zMsg, "%s TABLE %s", zMsg, pItem->zName);
    }

    if( pItem->zAlias ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s AS %s", zMsg, pItem->zAlias);
    }
    if( (flags & (WHERE_IPK|WHERE_VIRTUALTABLE))==0
     && pLoop->u.btree.pIndex!=0
    ){
      char *zWhere = explainIndexRange(db, pLoop, pItem->pTab);
      zMsg = sqlite3MAppendf(db, zMsg, "%s USING %s%sINDEX%s%s%s", zMsg, 
          ((flags & WHERE_TEMP_INDEX)?"AUTOMATIC ":""),
          ((flags & WHERE_IDX_ONLY)?"COVERING ":""),
          ((flags & WHERE_TEMP_INDEX)?"":" "),
          ((flags & WHERE_TEMP_INDEX)?"": pLoop->u.btree.pIndex->zName),
................................................................................

      if( flags&(WHERE_COLUMN_EQ|WHERE_COLUMN_IN) ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid=?)", zMsg);
      }else if( (flags&WHERE_BOTH_LIMIT)==WHERE_BOTH_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid>? AND rowid<?)", zMsg);
      }else if( flags&WHERE_BTM_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid>?)", zMsg);
      }else if( flags&WHERE_TOP_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid<?)", zMsg);
      }
    }
#ifndef SQLITE_OMIT_VIRTUALTABLE
    else if( (flags & WHERE_VIRTUALTABLE)!=0 ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s VIRTUAL TABLE INDEX %d:%s", zMsg,
                  pLoop->u.vtab.idxNum, pLoop->u.vtab.idxStr);
................................................................................
    */
    if( (nEq<pIdx->nColumn && bRev==(pIdx->aSortOrder[nEq]==SQLITE_SO_ASC))
     || (bRev && pIdx->nColumn==nEq)
    ){
      SWAP(WhereTerm *, pRangeEnd, pRangeStart);
    }

    testcase( pRangeStart && pRangeStart->eOperator & WO_LE );
    testcase( pRangeStart && pRangeStart->eOperator & WO_GE );
    testcase( pRangeEnd && pRangeEnd->eOperator & WO_LE );
    testcase( pRangeEnd && pRangeEnd->eOperator & WO_GE );
    startEq = !pRangeStart || pRangeStart->eOperator & (WO_LE|WO_GE);
    endEq =   !pRangeEnd || pRangeEnd->eOperator & (WO_LE|WO_GE);
    start_constraints = pRangeStart || nEq>0;

    /* Seek the index cursor to the start of the range. */
    nConstraint = nEq;
    if( pRangeStart ){
................................................................................
    if( pTerm->leftCursor!=iCur ) continue;
    pE = pTerm->pExpr;
    assert( !ExprHasProperty(pE, EP_FromJoin) );
    assert( (pTerm->prereqRight & newNotReady)!=0 );
    pAlt = findTerm(pWC, iCur, pTerm->u.leftColumn, notReady, WO_EQ|WO_IN, 0);
    if( pAlt==0 ) continue;
    if( pAlt->wtFlags & (TERM_CODED) ) continue;


    VdbeNoopComment((v, "begin transitive constraint"));
    sEq = *pAlt->pExpr;
    sEq.pLeft = pE->pLeft;
    sqlite3ExprIfFalse(pParse, &sEq, addrCont, SQLITE_JUMPIFNULL);
  }

  /* For a LEFT OUTER JOIN, generate code that will record the fact that
................................................................................
  ** is therefore the first and hence the best and should be retained.
  */
  if( (p = pBuilder->pBest)!=0 ){
    if( p->maskSelf!=0 ){
      WhereCost rCost = whereCostAdd(p->rRun,p->rSetup);
      WhereCost rTemplate = whereCostAdd(pTemplate->rRun,pTemplate->rSetup);
      if( rCost < rTemplate ){

        goto whereLoopInsert_noop;
      }
      if( rCost == rTemplate && p->prereq <= pTemplate->prereq ){
        goto whereLoopInsert_noop;
      }
    }
#if WHERETRACE_ENABLED
................................................................................
  */
  for(ppPrev=&pWInfo->pLoops, p=*ppPrev; p; ppPrev=&p->pNextLoop, p=*ppPrev){
    if( p->iTab!=pTemplate->iTab || p->iSortIdx!=pTemplate->iSortIdx ) continue;
    if( (p->prereq & pTemplate->prereq)==p->prereq
     && p->rSetup<=pTemplate->rSetup
     && p->rRun<=pTemplate->rRun
    ){


      /* p is equal or better than pTemplate */
      if( p->nLTerm<pTemplate->nLTerm
       && (p->wsFlags & WHERE_INDEXED)!=0
       && (pTemplate->wsFlags & WHERE_INDEXED)!=0
       && p->u.btree.pIndex==pTemplate->u.btree.pIndex
       && p->prereq==pTemplate->prereq
      ){
................................................................................
        break;
      }else{
        /* pTemplate is not helpful.
        ** Return without changing or adding anything */
        goto whereLoopInsert_noop;
      }
    }





    if( (p->prereq & pTemplate->prereq)==pTemplate->prereq
     && p->rSetup>=pTemplate->rSetup
     && p->rRun>=pTemplate->rRun
    ){
      /* Overwrite an existing WhereLoop with a better one */


      pNext = p->pNextLoop;
      break;
    }





  }

  /* 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
................................................................................
  WhereCost rLogSize;             /* Logarithm of table size */
  WhereTerm *pTop, *pBtm;         /* Top and bottom range constraints */

  pNew = pBuilder->pNew;
  if( db->mallocFailed ) return SQLITE_NOMEM;

  assert( (pNew->wsFlags & WHERE_VIRTUALTABLE)==0 );
  assert( pNew->u.btree.nEq<=pProbe->nColumn );
  assert( (pNew->wsFlags & WHERE_TOP_LIMIT)==0 );
  if( pNew->wsFlags & WHERE_BTM_LIMIT ){
    opMask = WO_LT|WO_LE;
  }else if( pProbe->tnum<=0 || (pSrc->jointype & JT_LEFT)!=0 ){
    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE;
  }else{
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);


  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    nRowEst = whereCost(pProbe->aiRowEst[pNew->u.btree.nEq+1]);
  }else{
    iCol = -1;
    nRowEst = 0;
  }
................................................................................
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;
      /* TUNING: IS NULL selects 2 rows */
      nIn = 10;  assert( 10==whereCost(2) );
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_GT|WO_GE) ){


      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;

    }else if( pTerm->eOperator & (WO_LT|WO_LE) ){


      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pTop = pTerm;
      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
................................................................................
** the table is used by an index.  Only the first 63 columns are considered.
*/
static Bitmask columnsInIndex(Index *pIdx){
  Bitmask m = 0;
  int j;
  for(j=pIdx->nColumn-1; j>=0; j--){
    int x = pIdx->aiColumn[j];


    if( x<BMS-1 ) m |= MASKBIT(x);
  }
  return m;
}


/*
................................................................................
  pNew->prereq = 0;
  pNew->rSetup = 0;
  pNew->wsFlags = WHERE_VIRTUALTABLE;
  pNew->nLTerm = 0;
  pNew->u.vtab.needFree = 0;
  pUsage = pIdxInfo->aConstraintUsage;
  nConstraint = pIdxInfo->nConstraint;
  if( whereLoopResize(db, pNew, nConstraint) ) return SQLITE_NOMEM;




  for(iPhase=0; iPhase<=3; iPhase++){
    if( !seenIn && (iPhase&1)!=0 ){
      iPhase++;
      if( iPhase>3 ) break;
    }
    if( !seenVar && iPhase>1 ) break;
................................................................................
      j = pIdxCons->iTermOffset;
      pTerm = &pWC->a[j];
      switch( iPhase ){
        case 0:    /* Constants without IN operator */
          pIdxCons->usable = 0;
          if( (pTerm->eOperator & WO_IN)!=0 ){
            seenIn = 1;

          }else if( pTerm->prereqRight!=0 ){
            seenVar = 1;
          }else{

            pIdxCons->usable = 1;
          }
          break;
        case 1:    /* Constants with IN operators */
          assert( seenIn );
          pIdxCons->usable = (pTerm->prereqRight==0);
          break;
................................................................................
         || j>=pWC->nTerm
         || pNew->aLTerm[iTerm]!=0
        ){
          rc = SQLITE_ERROR;
          sqlite3ErrorMsg(pParse, "%s.xBestIndex() malfunction", pTab->zName);
          goto whereLoopAddVtab_exit;
        }



        pTerm = &pWC->a[j];
        pNew->prereq |= pTerm->prereqRight;
        assert( iTerm<pNew->nLSlot );
        pNew->aLTerm[iTerm] = pTerm;
        if( iTerm>mxTerm ) mxTerm = iTerm;


        if( iTerm<16 && pUsage[i].omit ) pNew->u.vtab.omitMask |= 1<<iTerm;
        if( (pTerm->eOperator & WO_IN)!=0 ){
          if( pUsage[i].omit==0 ){
            /* Do not attempt to use an IN constraint if the virtual table
            ** says that the equivalent EQ constraint cannot be safely omitted.
            ** If we do attempt to use such a constraint, some rows might be
            ** repeated in the output. */
................................................................................
    testcase( nLoop>0 );  /* True when outer loops are one-row and match 
                          ** no ORDER BY terms */
    return pLast->u.vtab.isOrdered;
  }
  if( nLoop && OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ) return 0;

  nOrderBy = pOrderBy->nExpr;

  if( nOrderBy>BMS-1 ) return 0;  /* Cannot optimize overly large ORDER BYs */
  isOrderDistinct = 1;
  obDone = MASKBIT(nOrderBy)-1;
  orderDistinctMask = 0;
  ready = 0;
  for(iLoop=0; isOrderDistinct && obSat<obDone && iLoop<=nLoop; iLoop++){
    if( iLoop>0 ) ready |= pLoop->maskSelf;
................................................................................
      if( MASKBIT(i) & obSat ) continue;
      pOBExpr = sqlite3ExprSkipCollate(pOrderBy->a[i].pExpr);
      if( pOBExpr->op!=TK_COLUMN ) continue;
      if( pOBExpr->iTable!=iCur ) continue;
      pTerm = findTerm(&pWInfo->sWC, iCur, pOBExpr->iColumn,
                       ~ready, WO_EQ|WO_ISNULL, 0);
      if( pTerm==0 ) continue;
      testcase( pTerm->eOperator & WO_EQ );
      testcase( pTerm->eOperator & WO_ISNULL );
      if( pOBExpr->iColumn>=0 ){
        const char *z1, *z2;
        pColl = sqlite3ExprCollSeq(pWInfo->pParse, pOrderBy->a[i].pExpr);
        if( !pColl ) pColl = db->pDfltColl;
        z1 = pColl->zName;
        pColl = sqlite3ExprCollSeq(pWInfo->pParse, pTerm->pExpr);
        if( !pColl ) pColl = db->pDfltColl;
        z2 = pColl->zName;
................................................................................
      for(j=0; j<=nColumn; j++){
        u8 bOnce;   /* True to run the ORDER BY search loop */

        /* Skip over == and IS NULL terms */
        if( j<pLoop->u.btree.nEq
         && ((i = pLoop->aLTerm[j]->eOperator) & (WO_EQ|WO_ISNULL))!=0
        ){


          if( i & WO_ISNULL ) isOrderDistinct = 0;

          continue;  
        }

        /* Get the column number in the table (iColumn) and sort order
        ** (revIdx) for the j-th column of the index.
        */
        if( j<nColumn ){
          /* Normal index columns */
          iColumn = pIndex->aiColumn[j];
          revIdx = pIndex->aSortOrder[j];
          if( iColumn==pIndex->pTable->iPKey ) iColumn = -1;
        }else{
          /* The ROWID column at the end */

          iColumn = -1;
          revIdx = 0;
        }

        /* An unconstrained column that might be NULL means that this
        ** WhereLoop is not well-ordered 
        */
................................................................................
            if( !pColl ) pColl = db->pDfltColl;
            if( sqlite3StrICmp(pColl->zName, pIndex->azColl[j])!=0 ) continue;
          }
          isMatch = 1;
          break;
        }
        if( isMatch ){


          if( iColumn<0 ) distinctColumns = 1;

          obSat |= MASKBIT(i);
          if( (pWInfo->wctrlFlags & WHERE_GROUPBY)==0 ){
            /* Make sure the sort order is compatible in an ORDER BY clause.
            ** Sort order is irrelevant for a GROUP BY clause. */
            if( revSet ){
              if( (rev ^ revIdx)!=pOrderBy->a[i].sortOrder ) return 0;
            }else{
................................................................................
              rev = revIdx ^ pOrderBy->a[i].sortOrder;
              if( rev ) *pRevMask |= MASKBIT(iLoop);
              revSet = 1;
            }
          }
        }else{
          /* No match found */
          if( j==0 || j<nColumn ) isOrderDistinct = 0;



          break;
        }
      } /* end Loop over all index columns */
      if( distinctColumns ) isOrderDistinct = 1;
    } /* end-if not one-row */

    /* Mark off any other ORDER BY terms that reference pLoop */
................................................................................
          }
        }else{
          revMask = pFrom->revLoop;
        }
        /* Check to see if pWLoop should be added to the mxChoice best so far */
        for(jj=0, pTo=aTo; jj<nTo; jj++, pTo++){
          if( pTo->maskLoop==maskNew && pTo->isOrderedValid==isOrderedValid ){

            break;
          }
        }
        if( jj>=nTo ){
          if( nTo>=mxChoice && rCost>=mxCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
................................................................................
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
              sqlite3DebugPrintf("   vs %s cost=%-3d order=%c\n",
                  wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                  pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
            }
#endif

            continue;
          }

          /* A new and better score for a previously created equivalent path */
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf(
                "Update %s cost=%-3d order=%c",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
................................................................................
      /* noop */
    }else
#endif
    if( (pLoop->wsFlags & WHERE_IDX_ONLY)==0
         && (wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0 ){
      int op = pWInfo->okOnePass ? OP_OpenWrite : OP_OpenRead;
      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);
      testcase( pTab->nCol==BMS-1 );
      testcase( pTab->nCol==BMS );
      if( !pWInfo->okOnePass && pTab->nCol<BMS ){
        Bitmask b = pTabItem->colUsed;
        int n = 0;
        for(; b; b=b>>1, n++){}
        sqlite3VdbeChangeP4(v, sqlite3VdbeCurrentAddr(v)-1, 
                            SQLITE_INT_TO_PTR(n), P4_INT32);
        assert( n<=pTab->nCol );

  pIdx->pTable = pTable;
  n = 0;
  idxCols = 0;
  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){
    if( termCanDriveIndex(pTerm, pSrc, notReady) ){
      int iCol = pTerm->u.leftColumn;
      Bitmask cMask = iCol>=BMS ? MASKBIT(BMS-1) : MASKBIT(iCol);
      testcase( iCol==BMS-1 );
      testcase( iCol==BMS );
      if( (idxCols & cMask)==0 ){
        Expr *pX = pTerm->pExpr;
        idxCols |= cMask;
        pIdx->aiColumn[n] = pTerm->u.leftColumn;
        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);
        pIdx->azColl[n] = ALWAYS(pColl) ? pColl->zName : "BINARY";
        n++;
................................................................................
  Index *pIndex = pLoop->u.btree.pIndex;
  int nEq = pLoop->u.btree.nEq;
  int i, j;
  Column *aCol = pTab->aCol;
  int *aiColumn = pIndex->aiColumn;
  StrAccum txt;


  if( nEq==0 && (pLoop->wsFlags & (WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))==0 ){
    return 0;
  }
  sqlite3StrAccumInit(&txt, 0, 0, SQLITE_MAX_LENGTH);
  txt.db = db;
  sqlite3StrAccumAppend(&txt, " (", 2);
  for(i=0; i<nEq; i++){
................................................................................
      zMsg = sqlite3MAppendf(db, zMsg, "%s TABLE %s", zMsg, pItem->zName);
    }

    if( pItem->zAlias ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s AS %s", zMsg, pItem->zAlias);
    }
    if( (flags & (WHERE_IPK|WHERE_VIRTUALTABLE))==0
     && ALWAYS(pLoop->u.btree.pIndex!=0)
    ){
      char *zWhere = explainIndexRange(db, pLoop, pItem->pTab);
      zMsg = sqlite3MAppendf(db, zMsg, "%s USING %s%sINDEX%s%s%s", zMsg, 
          ((flags & WHERE_TEMP_INDEX)?"AUTOMATIC ":""),
          ((flags & WHERE_IDX_ONLY)?"COVERING ":""),
          ((flags & WHERE_TEMP_INDEX)?"":" "),
          ((flags & WHERE_TEMP_INDEX)?"": pLoop->u.btree.pIndex->zName),
................................................................................

      if( flags&(WHERE_COLUMN_EQ|WHERE_COLUMN_IN) ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid=?)", zMsg);
      }else if( (flags&WHERE_BOTH_LIMIT)==WHERE_BOTH_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid>? AND rowid<?)", zMsg);
      }else if( flags&WHERE_BTM_LIMIT ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid>?)", zMsg);
      }else if( ALWAYS(flags&WHERE_TOP_LIMIT) ){
        zMsg = sqlite3MAppendf(db, zMsg, "%s (rowid<?)", zMsg);
      }
    }
#ifndef SQLITE_OMIT_VIRTUALTABLE
    else if( (flags & WHERE_VIRTUALTABLE)!=0 ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s VIRTUAL TABLE INDEX %d:%s", zMsg,
                  pLoop->u.vtab.idxNum, pLoop->u.vtab.idxStr);
................................................................................
    */
    if( (nEq<pIdx->nColumn && bRev==(pIdx->aSortOrder[nEq]==SQLITE_SO_ASC))
     || (bRev && pIdx->nColumn==nEq)
    ){
      SWAP(WhereTerm *, pRangeEnd, pRangeStart);
    }

    testcase( pRangeStart && (pRangeStart->eOperator & WO_LE)!=0 );
    testcase( pRangeStart && (pRangeStart->eOperator & WO_GE)!=0 );
    testcase( pRangeEnd && (pRangeEnd->eOperator & WO_LE)!=0 );
    testcase( pRangeEnd && (pRangeEnd->eOperator & WO_GE)!=0 );
    startEq = !pRangeStart || pRangeStart->eOperator & (WO_LE|WO_GE);
    endEq =   !pRangeEnd || pRangeEnd->eOperator & (WO_LE|WO_GE);
    start_constraints = pRangeStart || nEq>0;

    /* Seek the index cursor to the start of the range. */
    nConstraint = nEq;
    if( pRangeStart ){
................................................................................
    if( pTerm->leftCursor!=iCur ) continue;
    pE = pTerm->pExpr;
    assert( !ExprHasProperty(pE, EP_FromJoin) );
    assert( (pTerm->prereqRight & newNotReady)!=0 );
    pAlt = findTerm(pWC, iCur, pTerm->u.leftColumn, notReady, WO_EQ|WO_IN, 0);
    if( pAlt==0 ) continue;
    if( pAlt->wtFlags & (TERM_CODED) ) continue;
    testcase( pAlt->eOperator & WO_EQ );
    testcase( pAlt->eOperator & WO_IN );
    VdbeNoopComment((v, "begin transitive constraint"));
    sEq = *pAlt->pExpr;
    sEq.pLeft = pE->pLeft;
    sqlite3ExprIfFalse(pParse, &sEq, addrCont, SQLITE_JUMPIFNULL);
  }

  /* For a LEFT OUTER JOIN, generate code that will record the fact that
................................................................................
  ** is therefore the first and hence the best and should be retained.
  */
  if( (p = pBuilder->pBest)!=0 ){
    if( p->maskSelf!=0 ){
      WhereCost rCost = whereCostAdd(p->rRun,p->rSetup);
      WhereCost rTemplate = whereCostAdd(pTemplate->rRun,pTemplate->rSetup);
      if( rCost < rTemplate ){
        testcase( rCost==rTemplate-1 );
        goto whereLoopInsert_noop;
      }
      if( rCost == rTemplate && p->prereq <= pTemplate->prereq ){
        goto whereLoopInsert_noop;
      }
    }
#if WHERETRACE_ENABLED
................................................................................
  */
  for(ppPrev=&pWInfo->pLoops, p=*ppPrev; p; ppPrev=&p->pNextLoop, p=*ppPrev){
    if( p->iTab!=pTemplate->iTab || p->iSortIdx!=pTemplate->iSortIdx ) continue;
    if( (p->prereq & pTemplate->prereq)==p->prereq
     && p->rSetup<=pTemplate->rSetup
     && p->rRun<=pTemplate->rRun
    ){
      testcase( p->rSetup==pTemplate->rSetup );
      testcase( p->rRun==pTemplate->rRun );
      /* p is equal or better than pTemplate */
      if( p->nLTerm<pTemplate->nLTerm
       && (p->wsFlags & WHERE_INDEXED)!=0
       && (pTemplate->wsFlags & WHERE_INDEXED)!=0
       && p->u.btree.pIndex==pTemplate->u.btree.pIndex
       && p->prereq==pTemplate->prereq
      ){
................................................................................
        break;
      }else{
        /* pTemplate is not helpful.
        ** Return without changing or adding anything */
        goto whereLoopInsert_noop;
      }
    }
    testcase( (p->prereq & pTemplate->prereq)==p->prereq 
              && p->rSetup==pTemplate->rSetup+1 );
    testcase( (p->prereq & pTemplate->prereq)==p->prereq
              && p->rSetup<=pTemplate->rSetup
              && p->rRun==pTemplate->rRun+1 );
    if( (p->prereq & pTemplate->prereq)==pTemplate->prereq
     && p->rSetup>=pTemplate->rSetup
     && p->rRun>=pTemplate->rRun
    ){
      /* Overwrite an existing WhereLoop with a better one */
      testcase( p->rSetup==pTemplate->rSetup );
      testcase( p->rRun==pTemplate->rRun );
      pNext = p->pNextLoop;
      break;
    }
    testcase( (p->prereq & pTemplate->prereq)==pTemplate->prereq
              && p->rSetup==pTemplate->rSetup-1 );
    testcase( (p->prereq & pTemplate->prereq)==pTemplate->prereq
              && p->rSetup>=pTemplate->rSetup-1
              && p->rRun==pTemplate->rRun-1 );
  }

  /* 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
................................................................................
  WhereCost rLogSize;             /* Logarithm of table size */
  WhereTerm *pTop, *pBtm;         /* Top and bottom range constraints */

  pNew = pBuilder->pNew;
  if( db->mallocFailed ) return SQLITE_NOMEM;

  assert( (pNew->wsFlags & WHERE_VIRTUALTABLE)==0 );

  assert( (pNew->wsFlags & WHERE_TOP_LIMIT)==0 );
  if( pNew->wsFlags & WHERE_BTM_LIMIT ){
    opMask = WO_LT|WO_LE;
  }else if( pProbe->tnum<=0 || (pSrc->jointype & JT_LEFT)!=0 ){
    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE;
  }else{
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  assert( pNew->u.btree.nEq<=pProbe->nColumn );
  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    nRowEst = whereCost(pProbe->aiRowEst[pNew->u.btree.nEq+1]);
  }else{
    iCol = -1;
    nRowEst = 0;
  }
................................................................................
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;
      /* TUNING: IS NULL selects 2 rows */
      nIn = 10;  assert( 10==whereCost(2) );
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_GT|WO_GE) ){
      testcase( pTerm->eOperator & WO_GT );
      testcase( pTerm->eOperator & WO_GE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else{
      assert( pTerm->eOperator & (WO_LT|WO_LE) );
      testcase( pTerm->eOperator & WO_LT );
      testcase( pTerm->eOperator & WO_LE );
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pTop = pTerm;
      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
................................................................................
** the table is used by an index.  Only the first 63 columns are considered.
*/
static Bitmask columnsInIndex(Index *pIdx){
  Bitmask m = 0;
  int j;
  for(j=pIdx->nColumn-1; j>=0; j--){
    int x = pIdx->aiColumn[j];
    testcase( x==BMS-1 );
    testcase( x==BMS-2 );
    if( x<BMS-1 ) m |= MASKBIT(x);
  }
  return m;
}


/*
................................................................................
  pNew->prereq = 0;
  pNew->rSetup = 0;
  pNew->wsFlags = WHERE_VIRTUALTABLE;
  pNew->nLTerm = 0;
  pNew->u.vtab.needFree = 0;
  pUsage = pIdxInfo->aConstraintUsage;
  nConstraint = pIdxInfo->nConstraint;
  if( whereLoopResize(db, pNew, nConstraint) ){
    sqlite3DbFree(db, pIdxInfo);
    return SQLITE_NOMEM;
  }

  for(iPhase=0; iPhase<=3; iPhase++){
    if( !seenIn && (iPhase&1)!=0 ){
      iPhase++;
      if( iPhase>3 ) break;
    }
    if( !seenVar && iPhase>1 ) break;
................................................................................
      j = pIdxCons->iTermOffset;
      pTerm = &pWC->a[j];
      switch( iPhase ){
        case 0:    /* Constants without IN operator */
          pIdxCons->usable = 0;
          if( (pTerm->eOperator & WO_IN)!=0 ){
            seenIn = 1;
          }
          if( pTerm->prereqRight!=0 ){
            seenVar = 1;

          }else if( (pTerm->eOperator & WO_IN)==0 ){
            pIdxCons->usable = 1;
          }
          break;
        case 1:    /* Constants with IN operators */
          assert( seenIn );
          pIdxCons->usable = (pTerm->prereqRight==0);
          break;
................................................................................
         || j>=pWC->nTerm
         || pNew->aLTerm[iTerm]!=0
        ){
          rc = SQLITE_ERROR;
          sqlite3ErrorMsg(pParse, "%s.xBestIndex() malfunction", pTab->zName);
          goto whereLoopAddVtab_exit;
        }
        testcase( iTerm==nConstraint-1 );
        testcase( j==0 );
        testcase( j==pWC->nTerm-1 );
        pTerm = &pWC->a[j];
        pNew->prereq |= pTerm->prereqRight;
        assert( iTerm<pNew->nLSlot );
        pNew->aLTerm[iTerm] = pTerm;
        if( iTerm>mxTerm ) mxTerm = iTerm;
        testcase( iTerm==15 );
        testcase( iTerm==16 );
        if( iTerm<16 && pUsage[i].omit ) pNew->u.vtab.omitMask |= 1<<iTerm;
        if( (pTerm->eOperator & WO_IN)!=0 ){
          if( pUsage[i].omit==0 ){
            /* Do not attempt to use an IN constraint if the virtual table
            ** says that the equivalent EQ constraint cannot be safely omitted.
            ** If we do attempt to use such a constraint, some rows might be
            ** repeated in the output. */
................................................................................
    testcase( nLoop>0 );  /* True when outer loops are one-row and match 
                          ** no ORDER BY terms */
    return pLast->u.vtab.isOrdered;
  }
  if( nLoop && OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ) return 0;

  nOrderBy = pOrderBy->nExpr;
  testcase( nOrderBy==BMS-1 );
  if( nOrderBy>BMS-1 ) return 0;  /* Cannot optimize overly large ORDER BYs */
  isOrderDistinct = 1;
  obDone = MASKBIT(nOrderBy)-1;
  orderDistinctMask = 0;
  ready = 0;
  for(iLoop=0; isOrderDistinct && obSat<obDone && iLoop<=nLoop; iLoop++){
    if( iLoop>0 ) ready |= pLoop->maskSelf;
................................................................................
      if( MASKBIT(i) & obSat ) continue;
      pOBExpr = sqlite3ExprSkipCollate(pOrderBy->a[i].pExpr);
      if( pOBExpr->op!=TK_COLUMN ) continue;
      if( pOBExpr->iTable!=iCur ) continue;
      pTerm = findTerm(&pWInfo->sWC, iCur, pOBExpr->iColumn,
                       ~ready, WO_EQ|WO_ISNULL, 0);
      if( pTerm==0 ) continue;


      if( (pTerm->eOperator&WO_EQ)!=0 && pOBExpr->iColumn>=0 ){
        const char *z1, *z2;
        pColl = sqlite3ExprCollSeq(pWInfo->pParse, pOrderBy->a[i].pExpr);
        if( !pColl ) pColl = db->pDfltColl;
        z1 = pColl->zName;
        pColl = sqlite3ExprCollSeq(pWInfo->pParse, pTerm->pExpr);
        if( !pColl ) pColl = db->pDfltColl;
        z2 = pColl->zName;
................................................................................
      for(j=0; j<=nColumn; j++){
        u8 bOnce;   /* True to run the ORDER BY search loop */

        /* Skip over == and IS NULL terms */
        if( j<pLoop->u.btree.nEq
         && ((i = pLoop->aLTerm[j]->eOperator) & (WO_EQ|WO_ISNULL))!=0
        ){
          if( i & WO_ISNULL ){
            testcase( isOrderDistinct );
            isOrderDistinct = 0;
          }
          continue;  
        }

        /* Get the column number in the table (iColumn) and sort order
        ** (revIdx) for the j-th column of the index.
        */
        if( j<nColumn ){
          /* Normal index columns */
          iColumn = pIndex->aiColumn[j];
          revIdx = pIndex->aSortOrder[j];
          if( iColumn==pIndex->pTable->iPKey ) iColumn = -1;
        }else{
          /* The ROWID column at the end */
          assert( j==nColumn );
          iColumn = -1;
          revIdx = 0;
        }

        /* An unconstrained column that might be NULL means that this
        ** WhereLoop is not well-ordered 
        */
................................................................................
            if( !pColl ) pColl = db->pDfltColl;
            if( sqlite3StrICmp(pColl->zName, pIndex->azColl[j])!=0 ) continue;
          }
          isMatch = 1;
          break;
        }
        if( isMatch ){
          if( iColumn<0 ){
            testcase( distinctColumns==0 );
            distinctColumns = 1;
          }
          obSat |= MASKBIT(i);
          if( (pWInfo->wctrlFlags & WHERE_GROUPBY)==0 ){
            /* Make sure the sort order is compatible in an ORDER BY clause.
            ** Sort order is irrelevant for a GROUP BY clause. */
            if( revSet ){
              if( (rev ^ revIdx)!=pOrderBy->a[i].sortOrder ) return 0;
            }else{
................................................................................
              rev = revIdx ^ pOrderBy->a[i].sortOrder;
              if( rev ) *pRevMask |= MASKBIT(iLoop);
              revSet = 1;
            }
          }
        }else{
          /* No match found */
          if( j==0 || j<nColumn ){
            testcase( isOrderDistinct!=0 );
            isOrderDistinct = 0;
          }
          break;
        }
      } /* end Loop over all index columns */
      if( distinctColumns ) isOrderDistinct = 1;
    } /* end-if not one-row */

    /* Mark off any other ORDER BY terms that reference pLoop */
................................................................................
          }
        }else{
          revMask = pFrom->revLoop;
        }
        /* Check to see if pWLoop should be added to the mxChoice best so far */
        for(jj=0, pTo=aTo; jj<nTo; jj++, pTo++){
          if( pTo->maskLoop==maskNew && pTo->isOrderedValid==isOrderedValid ){
            testcase( jj==nTo-1 );
            break;
          }
        }
        if( jj>=nTo ){
          if( nTo>=mxChoice && rCost>=mxCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
................................................................................
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
              sqlite3DebugPrintf("   vs %s cost=%-3d order=%c\n",
                  wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                  pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
            }
#endif
            testcase( pTo->rCost==rCost );
            continue;
          }
          testcase( pTo->rCost==rCost+1 );
          /* A new and better score for a previously created equivalent path */
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf(
                "Update %s cost=%-3d order=%c",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
................................................................................
      /* noop */
    }else
#endif
    if( (pLoop->wsFlags & WHERE_IDX_ONLY)==0
         && (wctrlFlags & WHERE_OMIT_OPEN_CLOSE)==0 ){
      int op = pWInfo->okOnePass ? OP_OpenWrite : OP_OpenRead;
      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);
      testcase( !pWInfo->okOnePass && pTab->nCol==BMS-1 );
      testcase( !pWInfo->okOnePass && pTab->nCol==BMS );
      if( !pWInfo->okOnePass && pTab->nCol<BMS ){
        Bitmask b = pTabItem->colUsed;
        int n = 0;
        for(; b; b=b>>1, n++){}
        sqlite3VdbeChangeP4(v, sqlite3VdbeCurrentAddr(v)-1, 
                            SQLITE_INT_TO_PTR(n), P4_INT32);
        assert( n<=pTab->nCol );