int i;
  for(i=0; i<nLoop; i++){ zName[i] = pPath->aLoop[i]->cId; }
  if( pLast ) zName[i++] = pLast->cId;
  zName[i] = 0;
  return zName;
}
#endif

/*
** Return the cost of sorting nRow rows, assuming that the keys have 
** nOrderby columns and that the first nSorted columns are already in
** order.
*/
static LogEst whereSortingCost(
  WhereInfo *pWInfo,
  LogEst nRow,
  int nOrderBy,
  int nSorted
){
  /* TUNING: Estimated cost of a full external sort, where N is 
  ** the number of rows to sort is:
  **
  **   cost = (3.0 * N * log(N)).
  ** 
  ** Or, if the order-by clause has X terms but only the last Y 
  ** terms are out of order, then block-sorting will reduce the 
  ** sorting cost to:
  **
  **   cost = (3.0 * N * log(N)) * (Y/X)
  **
  ** The (Y/X) term is implemented using stack variable rScale
  ** below.  */
  LogEst rScale, rSortCost;
  assert( nOrderBy>0 && 66==sqlite3LogEst(100) );
  rScale = sqlite3LogEst((nOrderBy-nSorted)*100/nOrderBy) - 66;
  rSortCost = nRow + estLog(nRow) + rScale + 16;

  /* TUNING: The cost of implementing DISTINCT using a B-TREE is
  ** similar but with a larger constant of proportionality. 
  ** Multiply by an additional factor of 3.0.  */
  if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){
    rSortCost += 16;
  }

  return rSortCost;
}

/*
** Given the list of WhereLoop objects at pWInfo->pLoops, this routine
** attempts to find the lowest cost path that visits each WhereLoop
** once.  This path is then loaded into the pWInfo->a[].pWLoop fields.
**
** Assume that the total number of output rows that will need to be sorted

  int nLoop;                /* Number of terms in the join */
  Parse *pParse;            /* Parsing context */
  sqlite3 *db;              /* The database connection */
  int iLoop;                /* Loop counter over the terms of the join */
  int ii, jj;               /* Loop counters */
  int mxI = 0;              /* Index of next entry to replace */
  int nOrderBy;             /* Number of ORDER BY clause terms */


  LogEst mxCost = 0;        /* Maximum cost of a set of paths */
  LogEst mxUnsorted = 0;    /* Maximum unsorted cost of a set of path */
  int nTo, nFrom;           /* Number of valid entries in aTo[] and aFrom[] */
  WherePath *aFrom;         /* All nFrom paths at the previous level */
  WherePath *aTo;           /* The nTo best paths at the current level */
  WherePath *pFrom;         /* An element of aFrom[] that we are working on */
  WherePath *pTo;           /* An element of aTo[] that we are working on */
  WhereLoop *pWLoop;        /* One of the WhereLoop objects */
  WhereLoop **pX;           /* Used to divy up the pSpace memory */
  LogEst *aSortCost = 0;    /* Sorting and partial sorting costs */
  char *pSpace;             /* Temporary memory used by this routine */
  int nSpace;               /* Bytes of space allocated at pSpace */

  pParse = pWInfo->pParse;
  db = pParse->db;
  nLoop = pWInfo->nLevel;
  /* TUNING: For simple queries, only the best path is tracked.
  ** For 2-way joins, the 5 best paths are followed.
  ** For joins of 3 or more tables, track the 10 best paths */
  mxChoice = (nLoop<=1) ? 1 : (nLoop==2 ? 5 : 10);
  assert( nLoop<=pWInfo->pTabList->nSrc );
  WHERETRACE(0x002, ("---- begin solver.  (nRowEst=%d)\n", nRowEst));

  /* If nRowEst is zero and there is an ORDER BY clause, ignore it. In this
  ** case the purpose of this call is to estimate the number of rows returned
  ** by the overall query. Once this estimate has been obtained, the caller
  ** will invoke this function a second time, passing the estimate as the
  ** nRowEst parameter.  */
  if( pWInfo->pOrderBy==0 || nRowEst==0 ){
    nOrderBy = 0;
  }else{
    nOrderBy = pWInfo->pOrderBy->nExpr;
  }

  /* Allocate and initialize space for aTo, aFrom and aSortCost[] */
  nSpace = (sizeof(WherePath)+sizeof(WhereLoop*)*nLoop)*mxChoice*2;
  nSpace += sizeof(LogEst) * nOrderBy;
  pSpace = sqlite3DbMallocRaw(db, nSpace);
  if( pSpace==0 ) return SQLITE_NOMEM;
  aTo = (WherePath*)pSpace;
  aFrom = aTo+mxChoice;
  memset(aFrom, 0, sizeof(aFrom[0]));
  pX = (WhereLoop**)(aFrom+mxChoice);
  for(ii=mxChoice*2, pFrom=aTo; ii>0; ii--, pFrom++, pX += nLoop){
    pFrom->aLoop = pX;
  }
  if( nOrderBy ){
    /* If there is an ORDER BY clause and it is not being ignored, set up
    ** space for the aSortCost[] array. Each element of the aSortCost array
    ** is either zero - meaning it has not yet been initialized - or the
    ** cost of sorting nRowEst rows of data where the first X terms of
    ** the ORDER BY clause are already in order, where X is the array 
    ** index.  */
    aSortCost = (LogEst*)pX;
    memset(aSortCost, 0, sizeof(LogEst) * nOrderBy);
  }
  assert( aSortCost==0 || &pSpace[nSpace]==(char*)&aSortCost[nOrderBy] );
  assert( aSortCost!=0 || &pSpace[nSpace]==(char*)pX );

  /* Seed the search with a single WherePath containing zero WhereLoops.
  **
  ** TUNING: Do not let the number of iterations go above 25.  If the cost
  ** of computing an automatic index is not paid back within the first 25
  ** rows, then do not use the automatic index. */
  aFrom[0].nRow = MIN(pParse->nQueryLoop, 46);  assert( 46==sqlite3LogEst(25) );
  nFrom = 1;




  assert( aFrom[0].isOrdered==0 );
  if( nOrderBy ){
    /* If nLoop is zero, then there are no FROM terms in the query. Since
    ** in this case the query may return a maximum of one row, the results
    ** are already in the requested order. Set isOrdered to nOrderBy to
    ** indicate this. Or, if nLoop is greater than zero, set isOrdered to
    ** -1, indicating that the result set may or may not be ordered, 
    ** depending on the loops added to the current plan.  */
    aFrom[0].isOrdered = nLoop>0 ? -1 : nOrderBy;

  }

  /* Compute successively longer WherePaths using the previous generation
  ** of WherePaths as the basis for the next.  Keep track of the mxChoice
  ** best paths at each generation */
  for(iLoop=0; iLoop<nLoop; iLoop++){
    nTo = 0;
    for(ii=0, pFrom=aFrom; ii<nFrom; ii++, pFrom++){
      for(pWLoop=pWInfo->pLoops; pWLoop; pWLoop=pWLoop->pNextLoop){
        LogEst nOut;                      /* Rows visited by (pFrom+pWLoop) */
        LogEst rCost;                     /* Cost of path (pFrom+pWLoop) */
        LogEst rUnsorted;                 /* Unsorted cost of (pFrom+pWLoop) */
        i8 isOrdered = pFrom->isOrdered;  /* isOrdered for (pFrom+pWLoop) */
        Bitmask maskNew;                  /* Mask of src visited by (..) */
        Bitmask revMask = 0;              /* Mask of rev-order loops for (..) */

        if( (pWLoop->prereq & ~pFrom->maskLoop)!=0 ) continue;
        if( (pWLoop->maskSelf & pFrom->maskLoop)!=0 ) continue;
        /* At this point, pWLoop is a candidate to be the next loop. 
        ** Compute its cost */
        rUnsorted = sqlite3LogEstAdd(pWLoop->rSetup,pWLoop->rRun + pFrom->nRow);
        rUnsorted = sqlite3LogEstAdd(rUnsorted, pFrom->rUnsorted);
        nOut = pFrom->nRow + pWLoop->nOut;
        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( isOrdered<0 ){
          isOrdered = wherePathSatisfiesOrderBy(pWInfo,
                       pWInfo->pOrderBy, pFrom, pWInfo->wctrlFlags,
                       iLoop, pWLoop, &revMask);
        }else{
          revMask = pFrom->revLoop;
        }
        if( isOrdered>=0 && isOrdered<nOrderBy ){













          if( aSortCost[isOrdered]==0 ){

            aSortCost[isOrdered] = whereSortingCost(
                pWInfo, nRowEst, nOrderBy, isOrdered
            );
          }




          rCost = sqlite3LogEstAdd(rUnsorted, aSortCost[isOrdered]);

          WHERETRACE(0x002,
              ("---- sort cost=%-3d (%d/%d) increases cost %3d to %-3d\n",
               aSortCost[isOrdered], (nOrderBy-isOrdered), nOrderBy, 
               rUnsorted, rCost));
        }else{
          rCost = rUnsorted;
        }



        /* Check to see if pWLoop should be added to the set of
        ** mxChoice best-so-far paths.
        **
        ** First look for an existing path among best-so-far paths
        ** that covers the same set of loops and has the same isOrdered
        ** setting as the current path candidate.
        **

            testcase( jj==nTo-1 );
            break;
          }
        }
        if( jj>=nTo ){
          /* None of the existing best-so-far paths match the candidate. */
          if( nTo>=mxChoice
           && (rCost>mxCost || (rCost==mxCost && rUnsorted>=mxUnsorted))
          ){
            /* The current candidate is no better than any of the mxChoice
            ** paths currently in the best-so-far buffer.  So discard
            ** this candidate as not viable. */
#ifdef WHERETRACE_ENABLED /* 0x4 */
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf("Skip   %s cost=%-3d,%3d order=%c\n",

#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;
            }
          }
        }
      }
    }

** at the end is the choosen query plan.
*/
struct WherePath {
  Bitmask maskLoop;     /* Bitmask of all WhereLoop objects in this path */
  Bitmask revLoop;      /* aLoop[]s that should be reversed for ORDER BY */
  LogEst nRow;          /* Estimated number of rows generated by this path */
  LogEst rCost;         /* Total cost of this path */
  LogEst rUnsorted;     /* Total cost of this path ignoring sorting costs */
  i8 isOrdered;         /* No. of ORDER BY terms satisfied. -1 for unknown */
  WhereLoop **aLoop;    /* Array of WhereLoop objects implementing this path */
};

/*
** The query generator uses an array of instances of this structure to
** help it analyze the subexpressions of the WHERE clause.  Each WHERE