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 */
      assert( pNew->nOut==saved_nOut );
      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, pNew);

      /* If the range constraint is the only constraint on the index and
      ** if the range constraint does not reduce the search space,
      ** then this is really just an index scan which has already
      ** been analyzed. */
      if( pNew->nOut>=saved_nOut && pNew->u.btree.nEq==0 ) continue;
    }
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    if( nInMul==0 
     && pProbe->nSample 
     && pNew->u.btree.nEq<=pProbe->nSampleCol
     && OptimizationEnabled(db, SQLITE_Stat3) 
    ){
................................................................................
#endif
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun =  sqlite3LogEstAdd(pNew->rRun,rLogSize>27 ? rLogSize-17 : 10);
    }
    /* Step cost for each output row */
    pNew->rRun = sqlite3LogEstAdd(pNew->rRun, pNew->nOut) + pProbe->szIdxRow;
    whereLoopOutputAdjust(pBuilder->pWC, pNew, pSrc->iCursor);
    rc = whereLoopInsert(pBuilder, pNew);
    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<(pProbe->nColumn + (pProbe->zName!=0))
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }
................................................................................
        pNew->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        /* TUNING: One-time cost for computing the automatic index is
        ** approximately 7*N*log2(N) where N is the number of rows in
        ** the table being indexed. */
        pNew->rSetup = rLogSize + rSize + 28;  assert( 28==sqlite3LogEst(7) );
        pNew->rSetup += pTab->szTabRow;
        /* 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 knowning 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) + pTab->szTabRow;
        pNew->wsFlags = WHERE_AUTO_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */
................................................................................
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      /* TUNING: Cost of full table scan is 3*(N + log2(N)).
      **  +  The extra 3 factor is to encourage the use of indexed lookups
      **     over full scans.  FIXME */
      pNew->rRun = sqlite3LogEstAdd(rSize,rLogSize) + 16 + pTab->szTabRow;
      whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);
      rc = whereLoopInsert(pBuilder, pNew);
      pNew->nOut = rSize;
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsInIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
      if( b
       || ( m==0
         && pProbe->bUnordered==0

         && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
         && sqlite3GlobalConfig.bUseCis
         && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
          )
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        if( m==0 ){
          /* TUNING: Cost of a covering index scan is K*(N + log2(N)).
          **  +  The extra factor K of between 1.1 (iScanRatio between 0
          **     and 9) and 2.8 (iScanRatio between 126 and 127) is added
          **     to encourage the use of indexed lookups.  FIXME
          */
          pNew->rRun = sqlite3LogEstAdd(rSize,rLogSize) + 10;

        }else{
          assert( b!=0 ); 
          /* TUNING: Cost of scanning a non-covering index is (N+1)*log2(N)
          ** which we will simplify to just N*log2(N) */
          pNew->rRun = rSize + rLogSize;
        }
        pNew->rRun += pProbe->szIdxRow;
        whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);
        rc = whereLoopInsert(pBuilder, pNew);
        pNew->nOut = rSize;
        if( rc ) break;
      }
    }

................................................................................
      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 = (u8)((pIdxInfo->nOrderBy!=0)
                                     && pIdxInfo->orderByConsumed);
      pNew->rSetup = 0;
      pNew->rRun = sqlite3LogEstFromDouble(pIdxInfo->estimatedCost) + 55;
      /* TUNING: Every virtual table query returns 25 rows */
      pNew->nOut = 46;  assert( 46==sqlite3LogEst(25) );
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 0;
      }
................................................................................
  if( pWInfo->pOrderBy==0 || nRowEst==0 ){
    aFrom[0].isOrderedValid = 1;
  }else{
    /* TUNING: Estimated cost of sorting is 48*N*log2(N) where N is the
    ** number of output rows. The 48 is the expected size of a row to sort. 
    ** FIXME:  compute a better estimate of the 48 multiplier based on the
    ** result set expressions. */
    rSortCost = nRowEst + estLog(nRowEst) + 55;
    WHERETRACE(0x002,("---- sort cost=%-3d\n", rSortCost));
  }

  /* 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++){

      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 */
      assert( pNew->nOut==saved_nOut );
      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, pNew);






    }
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    if( nInMul==0 
     && pProbe->nSample 
     && pNew->u.btree.nEq<=pProbe->nSampleCol
     && OptimizationEnabled(db, SQLITE_Stat3) 
    ){
................................................................................
#endif
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun =  sqlite3LogEstAdd(pNew->rRun,rLogSize>27 ? rLogSize-17 : 10);
    }
    /* Step cost for each output row */
    pNew->rRun = sqlite3LogEstAdd(pNew->rRun, pNew->nOut);
    whereLoopOutputAdjust(pBuilder->pWC, pNew, pSrc->iCursor);
    rc = whereLoopInsert(pBuilder, pNew);
    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<(pProbe->nColumn + (pProbe->zName!=0))
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }
................................................................................
        pNew->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        /* TUNING: One-time cost for computing the automatic index is
        ** approximately 7*N*log2(N) where N is the number of rows in
        ** the table being indexed. */
        pNew->rSetup = rLogSize + rSize + 28;  assert( 28==sqlite3LogEst(7) );

        /* 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 knowning how selective the index will ultimately be.  It would
        ** not be unreasonable to make this value much larger. */
        pNew->nOut = 43;  assert( 43==sqlite3LogEst(20) );
        pNew->rRun = sqlite3LogEstAdd(rLogSize,pNew->nOut);
        pNew->wsFlags = WHERE_AUTO_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }
#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */
................................................................................
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      /* TUNING: Cost of full table scan is 3*(N + log2(N)).
      **  +  The extra 3 factor is to encourage the use of indexed lookups
      **     over full scans.  FIXME */
      pNew->rRun = sqlite3LogEstAdd(rSize,rLogSize) + 16;
      whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);
      rc = whereLoopInsert(pBuilder, pNew);
      pNew->nOut = rSize;
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsInIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
      if( b
       || ( 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;
        if( m==0 ){
          /* TUNING: Cost of a covering index scan is K*(N + log2(N)).
          **  +  The extra factor K of between 1.1 and 3.0 that depends
          **     on the relative sizes of the table and the index.  K
          **     is smaller for smaller indices, thus favoring them.
          */
          pNew->rRun = sqlite3LogEstAdd(rSize,rLogSize) + 1 +
                        (15*pProbe->szIdxRow)/pTab->szTabRow;
        }else{
          assert( b!=0 ); 
          /* TUNING: Cost of scanning a non-covering index is (N+1)*log2(N)
          ** which we will simplify to just N*log2(N) */
          pNew->rRun = rSize + rLogSize;
        }

        whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);
        rc = whereLoopInsert(pBuilder, pNew);
        pNew->nOut = rSize;
        if( rc ) break;
      }
    }

................................................................................
      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 = (u8)((pIdxInfo->nOrderBy!=0)
                                     && pIdxInfo->orderByConsumed);
      pNew->rSetup = 0;
      pNew->rRun = sqlite3LogEstFromDouble(pIdxInfo->estimatedCost);
      /* TUNING: Every virtual table query returns 25 rows */
      pNew->nOut = 46;  assert( 46==sqlite3LogEst(25) );
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 0;
      }
................................................................................
  if( pWInfo->pOrderBy==0 || nRowEst==0 ){
    aFrom[0].isOrderedValid = 1;
  }else{
    /* TUNING: Estimated cost of sorting is 48*N*log2(N) where N is the
    ** number of output rows. The 48 is the expected size of a row to sort. 
    ** FIXME:  compute a better estimate of the 48 multiplier based on the
    ** result set expressions. */
    rSortCost = nRowEst + estLog(nRowEst);
    WHERETRACE(0x002,("---- sort cost=%-3d\n", rSortCost));
  }

  /* 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++){

     SELECT * FROM test1 a, test1 b LIMIT 1
  }
} {a.f1 11 a.f2 22 b.f1 11 b.f2 22}
do_test select1-6.9.7 {
  set x [execsql2 {
     SELECT * FROM test1 a, (select 5, 6) LIMIT 1
  }]
  regsub -all {subquery_[0-9a-fA-F]+_} $x {subquery} x
  set x
} {a.f1 11 a.f2 22 sqlite_subquery.5 5 sqlite_subquery.6 6}
do_test select1-6.9.8 {
  set x [execsql2 {
     SELECT * FROM test1 a, (select 5 AS x, 6 AS y) AS b LIMIT 1
  }]
  regsub -all {subquery_[0-9a-fA-F]+_} $x {subquery} x

     SELECT * FROM test1 a, test1 b LIMIT 1
  }
} {a.f1 11 a.f2 22 b.f1 11 b.f2 22}
do_test select1-6.9.7 {
  set x [execsql2 {
     SELECT * FROM test1 a, (select 5, 6) LIMIT 1
  }]
  regsub -all {sq_[0-9a-fA-F_]+} $x {subquery} x
  set x
} {a.f1 11 a.f2 22 sqlite_subquery.5 5 sqlite_subquery.6 6}
do_test select1-6.9.8 {
  set x [execsql2 {
     SELECT * FROM test1 a, (select 5 AS x, 6 AS y) AS b LIMIT 1
  }]
  regsub -all {subquery_[0-9a-fA-F]+_} $x {subquery} x

  catchsql {
    UPDATE t1 INDEXED BY t1b SET a=a+100
     WHERE (+b IS NULL AND c NOT NULL AND d NOT NULL)
        OR (b NOT NULL AND c IS NULL AND d NOT NULL)
        OR (b NOT NULL AND c NOT NULL AND d IS NULL)
  }
} {1 {no query solution}}











if {1} {









  do_test where9-6.8.3 {
    catchsql {
      UPDATE t1 INDEXED BY t1b SET a=a+100
       WHERE (b IS NULL AND c NOT NULL AND d NOT NULL)
          OR (b NOT NULL AND c IS NULL AND d NOT NULL)
          OR (b NOT NULL AND c NOT NULL AND d IS NULL)
    }

  catchsql {
    UPDATE t1 INDEXED BY t1b SET a=a+100
     WHERE (+b IS NULL AND c NOT NULL AND d NOT NULL)
        OR (b NOT NULL AND c IS NULL AND d NOT NULL)
        OR (b NOT NULL AND c NOT NULL AND d IS NULL)
  }
} {1 {no query solution}}
ifcapable stat4||stat3 {
  # When STAT3 is enabled, the "b NOT NULL" terms get translated
  # into b>NULL, which can be satified by the index t1b.  It is a very
  # expensive way to do the query, but it works, and so a solution is possible.
  do_test where9-6.8.3-stat4 {
    catchsql {
      UPDATE t1 INDEXED BY t1b SET a=a+100
       WHERE (b IS NULL AND c NOT NULL AND d NOT NULL)
          OR (b NOT NULL AND c IS NULL AND d NOT NULL)
          OR (b NOT NULL AND c NOT NULL AND d IS NULL)
    }
  } {0 {}}
  do_test where9-6.8.4-stat4 {
    catchsql {
      DELETE FROM t1 INDEXED BY t1b
       WHERE (b IS NULL AND c NOT NULL AND d NOT NULL)
          OR (b NOT NULL AND c IS NULL AND d NOT NULL)
          OR (b NOT NULL AND c NOT NULL AND d IS NULL)
    }
  } {0 {}}
} else {
  do_test where9-6.8.3 {
    catchsql {
      UPDATE t1 INDEXED BY t1b SET a=a+100
       WHERE (b IS NULL AND c NOT NULL AND d NOT NULL)
          OR (b NOT NULL AND c IS NULL AND d NOT NULL)
          OR (b NOT NULL AND c NOT NULL AND d IS NULL)
    }