typedef struct WhereAndInfo WhereAndInfo;
typedef struct WhereLevel WhereLevel;
typedef struct WhereLoop WhereLoop;
typedef struct WherePath WherePath;
typedef struct WhereTerm WhereTerm;
typedef struct WhereLoopBuilder WhereLoopBuilder;
typedef struct WhereScan WhereScan;
typedef float WhereCost;

/*
** For each nested loop in a WHERE clause implementation, the WhereInfo
** structure contains a single instance of this structure.  This structure
** is intended to be private to the where.c module and should not be
** access or modified by other modules.
**
................................................................................
      /* This index implies that the DISTINCT qualifier is redundant. */
      return 1;
    }
  }

  return 0;
}











































/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
** logN is a little off.
*/
static WhereCost estLog(WhereCost N){
  u32 a;
  assert( sizeof(WhereCost)==4 );  /* 32-bit float input */
  if( N<=0.0 ) return 0.0;
  memcpy(&a, &N, 4);
  return ((a >>= 23)-127)*0.3;
}

/*
** 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.
................................................................................
  tRowcnt *aStat              /* OUT: stats written here */
){
  tRowcnt n;
  IndexSample *aSample;
  int i, eType;
  int isEq = 0;
  i64 v;
  WhereCost r, rS;

  assert( roundUp==0 || roundUp==1 );
  assert( pIdx->nSample>0 );
  if( pVal==0 ) return SQLITE_ERROR;
  n = pIdx->aiRowEst[0];
  aSample = pIdx->aSample;
  eType = sqlite3_value_type(pVal);
................................................................................
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      if( iUpper<=iLower ){
        *pRangeDiv = (WhereCost)p->aiRowEst[0];
      }else{
        *pRangeDiv = (WhereCost)p->aiRowEst[0]/(WhereCost)(iUpper - iLower);
      }
      /*WHERETRACE(("range scan regions: %u..%u  div=%g\n",
                  (u32)iLower, (u32)iUpper, *pRangeDiv));*/
      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = (WhereCost)1;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ) *pRangeDiv *= (WhereCost)4;


  if( pUpper ) *pRangeDiv *= (WhereCost)4;


  return rc;
}

#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
** an equality constraint x=VALUE and where that VALUE occurs in
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  WhereCost *pnRow     /* Write the revised row estimate here */
){
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */

  assert( p->aSample!=0 );
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  WhereCost *pnRow     /* Write the revised row estimate here */
){
  int rc = SQLITE_OK;         /* Subfunction return code */
  WhereCost nEst;                /* Number of rows for a single term */
  WhereCost nRowEst = (WhereCost)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 = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, p, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
  }
................................................................................
  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */
){
  if( pParse->explain==2 ){
    struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];
    Vdbe *v = pParse->pVdbe;      /* VM being constructed */
    sqlite3 *db = pParse->db;     /* Database handle */
    char *zMsg;                   /* Text to add to EQP output */
    sqlite3_int64 nRow;           /* Expected number of rows visited by scan */
    int iId = pParse->iSelectId;  /* Select id (left-most output column) */
    int isSearch;                 /* True for a SEARCH. False for SCAN. */
    WhereLoop *pLoop;             /* The controlling WhereLoop object */
    u32 flags;                    /* Flags that describe this loop */

    pLoop = pLevel->pWLoop;
    flags = pLoop->wsFlags;
................................................................................
    }
#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);
    }
#endif
    if( wctrlFlags&(WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX) ){
      testcase( wctrlFlags & WHERE_ORDERBY_MIN );
      nRow = 1;
    }else{
      nRow = (sqlite3_int64)pLoop->nOut;
    }
    zMsg = sqlite3MAppendf(db, zMsg, "%s (~%lld rows)", zMsg, nRow);
    sqlite3VdbeAddOp4(v, OP_Explain, iId, iLevel, iFrom, zMsg, P4_DYNAMIC);
  }
}
#else
# define explainOneScan(u,v,w,x,y,z)
#endif /* SQLITE_OMIT_EXPLAIN */

................................................................................
}

#ifdef WHERETRACE_ENABLED
/*
** Print a WhereLoop object for debugging purposes
*/
static void whereLoopPrint(WhereLoop *p, SrcList *pTabList){
  int nb = 2*((pTabList->nSrc+15)/16);
  struct SrcList_item *pItem = pTabList->a + p->iTab;
  Table *pTab = pItem->pTab;
  sqlite3DebugPrintf("%c %2d.%0*llx.%0*llx", p->cId,
                     p->iTab, nb, p->maskSelf, nb, p->prereq);
  sqlite3DebugPrintf(" %8s",
                     pItem->zAlias ? pItem->zAlias : pTab->zName);
  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){
................................................................................
    }else{
      z = sqlite3_mprintf("(%d,%x)", p->u.vtab.idxNum, p->u.vtab.omitMask);
    }
    sqlite3DebugPrintf(" %-15s", z);
    sqlite3_free(z);
  }
  sqlite3DebugPrintf(" fg %05x N %d", p->wsFlags, p->nLTerm);
  sqlite3DebugPrintf(" cost %.2g,%.2g,%.2g\n",
                     p->prereq, p->rSetup, p->rRun, p->nOut);
}
#endif

/*
** Convert bulk memory into a valid WhereLoop that can be passed
** to whereLoopClear harmlessly.
*/
................................................................................
  /* If pBuilder->pBest is defined, then only keep track of the single
  ** best WhereLoop.  pBuilder->pBest->maskSelf==0 indicates that no
  ** prior WhereLoops have been evaluated and that the current pTemplate
  ** is therefore the first and hence the best and should be retained.
  */
  if( (p = pBuilder->pBest)!=0 ){
    if( p->maskSelf!=0 ){
      WhereCost rCost = p->rRun + p->rSetup;
      WhereCost rTemplate = pTemplate->rRun + pTemplate->rSetup;
      if( rCost < rTemplate ){
        goto whereLoopInsert_noop;
      }
      if( rCost == rTemplate && p->prereq <= pTemplate->prereq ){
        goto whereLoopInsert_noop;
      }
    }
................................................................................
** If pProbe->tnum==0, that means pIndex is a fake index used for the
** INTEGER PRIMARY KEY.
*/
static int whereLoopAddBtreeIndex(
  WhereLoopBuilder *pBuilder,     /* The WhereLoop factory */
  struct SrcList_item *pSrc,      /* FROM clause term being analyzed */
  Index *pProbe,                  /* An index on pSrc */
  int nInMul                      /* 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 */
................................................................................
  Bitmask saved_prereq;           /* Original value of pNew->prereq */
  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
  int saved_nEq;                  /* Original value of pNew->u.btree.nEq */
  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */
  WhereCost saved_nOut;           /* Original value of pNew->nOut */
  int iCol;                       /* Index of the column in the table */
  int rc = SQLITE_OK;             /* Return code */
  tRowcnt iRowEst;                /* Estimated index selectivity */
  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 );
................................................................................
  }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];
    iRowEst = pProbe->aiRowEst[pNew->u.btree.nEq+1];
  }else{
    iCol = -1;
    iRowEst = 1;
  }
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  saved_nEq = pNew->u.btree.nEq;
  saved_nLTerm = pNew->nLTerm;
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = (WhereCost)0;
  rLogSize = estLog(pProbe->aiRowEst[0]);
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 1;
    if( pTerm->prereqRight & pNew->maskSelf ) continue;
    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize;
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
      pNew->wsFlags |= WHERE_COLUMN_IN;
      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
        /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
        nIn = 25;
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = pExpr->x.pList->nExpr;
      }
      pNew->rRun *= nIn;
      pNew->u.btree.nEq++;
      pNew->nOut = (WhereCost)iRowEst * nInMul * nIn;
    }else if( pTerm->eOperator & (WO_EQ) ){
      assert( (pNew->wsFlags & (WHERE_COLUMN_NULL|WHERE_COLUMN_IN))!=0
                  || nInMul==1 );
      pNew->wsFlags |= WHERE_COLUMN_EQ;
      if( iCol<0  
       || (pProbe->onError!=OE_None && nInMul==1
           && pNew->u.btree.nEq==pProbe->nColumn-1)
      ){
        testcase( pNew->wsFlags & WHERE_COLUMN_IN );
        pNew->wsFlags |= WHERE_ONEROW;
      }
      pNew->u.btree.nEq++;
      pNew->nOut = (WhereCost)iRowEst * nInMul;
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;
      nIn = 2;  /* Assume IS NULL matches two rows */
      pNew->nOut = (WhereCost)iRowEst * 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;
................................................................................
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
      WhereCost rDiv;
      whereRangeScanEst(pParse, pProbe, pNew->u.btree.nEq,
                        pBtm, pTop, &rDiv);
      pNew->nOut = saved_nOut/rDiv;
    }
#ifdef SQLITE_ENABLE_STAT3
    if( pNew->u.btree.nEq==1 && pProbe->nSample ){

      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        rc = whereEqualScanEst(pParse, pProbe, pTerm->pExpr->pRight,
                               &pNew->nOut);
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pTerm->pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pProbe, pTerm->pExpr->x.pList,
                             &pNew->nOut);

      }

    }
#endif
    if( pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK) ){
      pNew->rRun += pNew->nOut;  /* Unit step cost to reach each row */

    }else{
      /* Each row involves a step of the index, then a binary search of
      ** the main table */


      pNew->rRun += pNew->nOut*(1 + rLogSize);
    }
    /* TBD: Adjust nOut for additional constraints */
    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->prereq = saved_prereq;
  pNew->u.btree.nEq = saved_nEq;
  pNew->wsFlags = saved_wsFlags;
  pNew->nOut = saved_nOut;
  pNew->nLTerm = saved_nLTerm;
................................................................................
  int 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 */
  WhereCost rSize;               /* number of rows in the table */
  WhereCost rLogSize;            /* Logarithm of the number of rows in the table */
  
  pNew = pBuilder->pNew;
  pWInfo = pBuilder->pWInfo;
  pTabList = pWInfo->pTabList;
  pSrc = pTabList->a + pNew->iTab;
  assert( !IsVirtual(pSrc->pTab) );

................................................................................
    if( pSrc->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 = (WhereCost)pSrc->pTab->nRowEst;
  rLogSize = estLog(rSize);

  /* Automatic indexes */
  if( !pBuilder->pBest
   && pTabList->nSrc>1
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0 
   && !pSrc->viaCoroutine
................................................................................
    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->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        pNew->rSetup = 20*rLogSize*pSrc->pTab->nRowEst;
        pNew->nOut = (WhereCost)10;
        pNew->rRun = rLogSize + pNew->nOut;

        pNew->wsFlags = WHERE_TEMP_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }

  /* Loop over all indices
  */
  for(; rc==SQLITE_OK && pProbe; pProbe=pProbe->pNext, iSortIdx++){
    pNew->u.btree.nEq = 0;
    pNew->nLTerm = 0;
    pNew->iSortIdx = 0;
    pNew->rSetup = (WhereCost)0;
    pNew->prereq = mExtra;
    pNew->u.btree.pIndex = pProbe;
    b = indexMightHelpWithOrderBy(pBuilder, pProbe, pSrc->iCursor);
    if( pProbe->tnum<=0 ){
      /* Integer primary key index */
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      pNew->nOut = rSize;
      pNew->rRun = (rSize + rLogSize)*(3+b); /* 4x penalty for a full-scan */
      rc = whereLoopInsert(pBuilder, pNew);
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsUsedByIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
................................................................................
       && pProbe->bUnordered==0
       && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
       && sqlite3GlobalConfig.bUseCis
       && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        pNew->nOut = rSize;
        pNew->rRun = (m==0) ? (rSize + rLogSize)*(1+b) : (rSize*rLogSize);
        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }
    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 1);

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;
  }
  return rc;
}
................................................................................
      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 = (u8)((pIdxInfo->nOrderBy!=0)
                                     && pIdxInfo->orderByConsumed);
      pNew->rSetup = (WhereCost)0;
      pNew->rRun = pIdxInfo->estimatedCost;
      pNew->nOut = (WhereCost)25;
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 0;
      }
    }
  }  
................................................................................
        sBest.rRun = 0;
        if( IsVirtual(pItem->pTab) ){
          rc = whereLoopAddVirtual(&sSubBuild, mExtra);
        }else{
          rc = whereLoopAddBtree(&sSubBuild, mExtra);
        }
        if( sBest.maskSelf==0 ) break;
        assert( sBest.rSetup==(WhereCost)0 );
        rTotal += sBest.rRun;
        nRow += sBest.nOut;
        prereq |= sBest.prereq;
      }
      assert( pNew->nLSlot>=1 );
      pNew->nLTerm = 1;
      pNew->aLTerm[0] = pTerm;
      pNew->wsFlags = WHERE_MULTI_OR;
      pNew->rSetup = (WhereCost)0;
      pNew->rRun = rTotal;
      pNew->nOut = nRow;
      pNew->prereq = prereq;
      memset(&pNew->u, 0, sizeof(pNew->u));
      rc = whereLoopInsert(pBuilder, pNew);
      whereLoopClear(pWInfo->pParse->db, &sBest);
    }
................................................................................
  Bitmask mPrior = 0;
  int iTab;
  SrcList *pTabList = pWInfo->pTabList;
  struct SrcList_item *pItem;
  sqlite3 *db = pWInfo->pParse->db;
  int nTabList = pWInfo->nLevel;
  int rc = SQLITE_OK;
  WhereLoop *pNew, sNew;

  /* Loop over the tables in the join, from left to right */
  pBuilder->pNew = pNew = &sNew;
  whereLoopInit(pNew);
  for(iTab=0, pItem=pTabList->a; iTab<nTabList; iTab++, pItem++){
    pNew->iTab = iTab;
    pNew->maskSelf = getMask(&pWInfo->sMaskSet, pItem->iCursor);
    if( (pItem->jointype & (JT_LEFT|JT_CROSS))!=0 ){
      mExtra = mPrior;
    }
................................................................................
    if( rc==SQLITE_OK ){
      rc = whereLoopAddOr(pBuilder, mExtra);
    }
    mPrior |= pNew->maskSelf;
    if( rc || db->mallocFailed ) break;
  }
  whereLoopClear(db, pNew);
  pBuilder->pNew = 0;
  return rc;
}

/*
** Examine a WherePath (with the addition of the extra WhereLoop of the 5th
** parameters) to see if it outputs rows in the requested ORDER BY
** (or GROUP BY) without requiring a separate source operation.  Return:
................................................................................
  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;
  }

  /* Seed the search with a single WherePath containing zero WhereLoops */
  aFrom[0].nRow = (WhereCost)1;
  nFrom = 1;

  /* Precompute the cost of sorting the final result set, if the caller
  ** to sqlite3WhereBegin() was concerned about sorting */
  rSortCost = (WhereCost)0;
  if( pWInfo->pOrderBy==0 || nRowEst<=0.0 ){
    aFrom[0].isOrderedValid = 1;
  }else{
    /* Compute an estimate on the cost to sort the entire result set */
    rSortCost = nRowEst*estLog(nRowEst);
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      sqlite3DebugPrintf("---- sort cost=%-7.2g\n", rSortCost);
    }
#endif
  }

  /* 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 */
................................................................................
        Bitmask revMask = 0;
        u8 isOrderedValid = pFrom->isOrderedValid;
        u8 isOrdered = pFrom->isOrdered;
        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 */
        rCost = pWLoop->rSetup + pWLoop->rRun*pFrom->nRow + pFrom->rCost;

        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( !isOrderedValid ){
          switch( wherePathSatisfiesOrderBy(pWInfo, pFrom, iLoop, iLoop==nLoop-1,
                                            pWLoop, &revMask) ){
            case 1:  /* Yes.  pFrom+pWLoop does satisfy the ORDER BY clause */
              isOrdered = 1;
              isOrderedValid = 1;
              break;
            case 0:  /* No.  pFrom+pWLoop will require a separate sort */
              isOrdered = 0;
              isOrderedValid = 1;
              rCost += rSortCost;
              break;
            default: /* Cannot tell yet.  Try again on the next iteration */
              break;
          }
        }else{
          revMask = pFrom->revLoop;
        }
................................................................................
            break;
          }
        }
        if( jj>=nTo ){
          if( nTo>=mxChoice && rCost>=mxCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf("Skip   %s cost=%-7.2g order=%c\n",
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
            }
#endif
            continue;
          }
          /* Add a new Path to the aTo[] set */
................................................................................
          }else{
            /* New path replaces the prior worst to keep count below mxChoice */
            for(jj=nTo-1; aTo[jj].rCost<mxCost; jj--){ assert(jj>0); }
          }
          pTo = &aTo[jj];
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf("New    %s cost=%-7.2g order=%c\n",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
          }
#endif
        }else{
          if( pTo->rCost<=rCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf(
                  "Skip   %s cost=%-7.2g order=%c",
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
              sqlite3DebugPrintf("   vs %s cost=%-7.2g 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=%-7.2g order=%c",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
            sqlite3DebugPrintf("  was %s cost=%-7.2g order=%c\n",
                wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : '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 = pFrom->nRow * pWLoop->nOut;
        pTo->rCost = rCost;
        pTo->isOrderedValid = isOrderedValid;
        pTo->isOrdered = isOrdered;
        memcpy(pTo->aLoop, pFrom->aLoop, sizeof(WhereLoop*)*iLoop);
        pTo->aLoop[iLoop] = pWLoop;
        if( nTo>=mxChoice ){
          mxCost = aTo[0].rCost;
................................................................................
      }
    }

#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      sqlite3DebugPrintf("---- after round %d ----\n", iLoop);
      for(ii=0, pTo=aTo; ii<nTo; ii++, pTo++){
        sqlite3DebugPrintf(" %s cost=%-7.2g nrow=%-7.2g order=%c",
           wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
           pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
        if( pTo->isOrderedValid && pTo->isOrdered ){
          sqlite3DebugPrintf(" rev=0x%llx\n", pTo->revLoop);
        }else{
          sqlite3DebugPrintf("\n");
        }
................................................................................
** 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 whereSimpleFastCase(WhereLoopBuilder *pBuilder){
  WhereInfo *pWInfo;
  struct SrcList_item *pItem;
  WhereClause *pWC;
  WhereTerm *pTerm;
  WhereLoop *pLoop;
  int iCur;
  int j;
................................................................................
  pLoop->wsFlags = 0;
  pTerm = findTerm(pWC, iCur, -1, 0, WO_EQ, 0);
  if( pTerm ){
    pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_IPK|WHERE_ONEROW;
    pLoop->aLTerm[0] = pTerm;
    pLoop->nLTerm = 1;
    pLoop->u.btree.nEq = 1;
    pLoop->rRun = (WhereCost)10;
  }else{
    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
      if( pIdx->onError==OE_None ) continue;
      for(j=0; j<pIdx->nColumn; j++){
        pTerm = findTerm(pWC, iCur, pIdx->aiColumn[j], 0, WO_EQ, pIdx);
        if( pTerm==0 ) break;
        whereLoopResize(pWInfo->pParse->db, pLoop, j);
................................................................................
      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;
      if( (pItem->colUsed & ~columnsUsedByIndex(pIdx))==0 ){
        pLoop->wsFlags |= WHERE_IDX_ONLY;
      }
      pLoop->nLTerm = j;
      pLoop->u.btree.nEq = j;
      pLoop->u.btree.pIndex = pIdx;
      pLoop->rRun = (WhereCost)15;
      break;
    }
  }
  if( pLoop->wsFlags ){
    pLoop->nOut = (WhereCost)1;
    pWInfo->a[0].pWLoop = pLoop;
    pLoop->maskSelf = getMask(&pWInfo->sMaskSet, iCur);
................................................................................
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = &pWInfo->sMaskSet;
  sWLB.pWInfo = pWInfo;
  sWLB.pWC = &pWInfo->sWC;
  sWLB.pNew = (WhereLoop*)&pWInfo->a[nTabList];
  whereLoopInit(sWLB.pNew);




  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via
  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */
  if( OptimizationDisabled(db, SQLITE_DistinctOpt) ) pDistinct = 0;

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
................................................................................
  if( pDistinct && isDistinctRedundant(pParse,pTabList,&pWInfo->sWC,pDistinct) ){
    pDistinct = 0;
    pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
  }

  /* Construct the WhereLoop objects */
  WHERETRACE(("*** Optimizer Start ***\n"));
  if( nTabList!=1 || whereSimpleFastCase(&sWLB)==0 ){
    rc = whereLoopAddAll(&sWLB);
    if( rc ) goto whereBeginError;
  
    /* Display all of the WhereLoop objects if wheretrace is enabled */
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace ){
      WhereLoop *p;

typedef struct WhereAndInfo WhereAndInfo;
typedef struct WhereLevel WhereLevel;
typedef struct WhereLoop WhereLoop;
typedef struct WherePath WherePath;
typedef struct WhereTerm WhereTerm;
typedef struct WhereLoopBuilder WhereLoopBuilder;
typedef struct WhereScan WhereScan;
typedef unsigned short int WhereCost;  /* 10 times log2() of run-time */

/*
** For each nested loop in a WHERE clause implementation, the WhereInfo
** structure contains a single instance of this structure.  This structure
** is intended to be private to the where.c module and should not be
** access or modified by other modules.
**
................................................................................
      /* This index implies that the DISTINCT qualifier is redundant. */
      return 1;
    }
  }

  return 0;
}

/* 
** The sum of two WhereCosts
*/
static WhereCost whereCostAdd(WhereCost a, WhereCost b){
  static const unsigned char x[] = {
     10, 10,                         /* 0,1 */
      9, 9,                          /* 2,3 */
      8, 8,                          /* 4,5 */
      7, 7, 7,                       /* 6,7,8 */
      6, 6, 6,                       /* 9,10,11 */
      5, 5, 5,                       /* 12-14 */
      4, 4, 4, 4,                    /* 15-18 */
      3, 3, 3, 3, 3, 3,              /* 19-24 */
      2, 2, 2, 2, 2, 2, 2,           /* 25-31 */
  };
  if( a>=b ){
    if( a>b+49 ) return a;
    if( a>b+31 ) return a+1;
    return a+x[a-b];
  }else{
    if( b>a+49 ) return b;
    if( b>a+31 ) return b+1;
    return b+x[b-a];
  }
}

/*
** Convert an integer into a WhereCost
*/
static WhereCost whereCostFromInt(tRowcnt x){
  static WhereCost a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
  WhereCost y = 40;
  if( x<8 ){
    if( x<2 ) return 0;
    while( x<8 ){  y -= 10; x <<= 1; }
  }else{
    while( x>255 ){ y += 40; x >>= 4; }
    while( x>15 ){  y += 10; x >>= 1; }
  }
  return a[x&7] + y - 10;
}

/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
** logN is a little off.
*/
static WhereCost estLog(WhereCost N){
  return whereCostFromInt(N) - 33;




}

/*
** 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.
................................................................................
  tRowcnt *aStat              /* OUT: stats written here */
){
  tRowcnt n;
  IndexSample *aSample;
  int i, eType;
  int isEq = 0;
  i64 v;
  double r, rS;

  assert( roundUp==0 || roundUp==1 );
  assert( pIdx->nSample>0 );
  if( pVal==0 ) return SQLITE_ERROR;
  n = pIdx->aiRowEst[0];
  aSample = pIdx->aSample;
  eType = sqlite3_value_type(pVal);
................................................................................
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      WhereCost iBase = whereCostFromInt(p->aiRowEst[0]);
      if( iUpper>iLower ){
        iBase -= whereCostFromInt(iUpper - iLower);
      }
      *pRangeDiv = iBase;
      /*WHERETRACE(("range scan regions: %u..%u  div=%g\n",
                  (u32)iLower, (u32)iUpper, *pRangeDiv));*/
      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = 0;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
    *pRangeDiv += 20;  assert( 20==whereCostFromInt(4) );
  }
  if( pUpper ){
    *pRangeDiv += 20;  assert( 20==whereCostFromInt(4) );
  }
  return rc;
}

#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
** an equality constraint x=VALUE and where that VALUE occurs in
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */

  assert( p->aSample!=0 );
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  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 = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, p, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
  }
................................................................................
  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */
){
  if( pParse->explain==2 ){
    struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];
    Vdbe *v = pParse->pVdbe;      /* VM being constructed */
    sqlite3 *db = pParse->db;     /* Database handle */
    char *zMsg;                   /* Text to add to EQP output */

    int iId = pParse->iSelectId;  /* Select id (left-most output column) */
    int isSearch;                 /* True for a SEARCH. False for SCAN. */
    WhereLoop *pLoop;             /* The controlling WhereLoop object */
    u32 flags;                    /* Flags that describe this loop */

    pLoop = pLevel->pWLoop;
    flags = pLoop->wsFlags;
................................................................................
    }
#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);
    }
#endif






    zMsg = sqlite3MAppendf(db, zMsg, "%s", zMsg);
    sqlite3VdbeAddOp4(v, OP_Explain, iId, iLevel, iFrom, zMsg, P4_DYNAMIC);
  }
}
#else
# define explainOneScan(u,v,w,x,y,z)
#endif /* SQLITE_OMIT_EXPLAIN */

................................................................................
}

#ifdef WHERETRACE_ENABLED
/*
** Print a WhereLoop object for debugging purposes
*/
static void whereLoopPrint(WhereLoop *p, SrcList *pTabList){
  int nb = 1+(pTabList->nSrc+7)/8;
  struct SrcList_item *pItem = pTabList->a + p->iTab;
  Table *pTab = pItem->pTab;
  sqlite3DebugPrintf("%c %2d.%0*llx.%0*llx", p->cId,
                     p->iTab, nb, p->maskSelf, nb, p->prereq);
  sqlite3DebugPrintf(" %8s",
                     pItem->zAlias ? pItem->zAlias : pTab->zName);
  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){
................................................................................
    }else{
      z = sqlite3_mprintf("(%d,%x)", p->u.vtab.idxNum, p->u.vtab.omitMask);
    }
    sqlite3DebugPrintf(" %-15s", z);
    sqlite3_free(z);
  }
  sqlite3DebugPrintf(" fg %05x N %d", p->wsFlags, p->nLTerm);

  sqlite3DebugPrintf(" cost %d,%d,%d\n", p->rSetup, p->rRun, p->nOut);
}
#endif

/*
** Convert bulk memory into a valid WhereLoop that can be passed
** to whereLoopClear harmlessly.
*/
................................................................................
  /* If pBuilder->pBest is defined, then only keep track of the single
  ** best WhereLoop.  pBuilder->pBest->maskSelf==0 indicates that no
  ** prior WhereLoops have been evaluated and that the current pTemplate
  ** 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 pProbe->tnum==0, that means pIndex is a fake index used for the
** INTEGER PRIMARY KEY.
*/
static int whereLoopAddBtreeIndex(
  WhereLoopBuilder *pBuilder,     /* The WhereLoop factory */
  struct SrcList_item *pSrc,      /* FROM clause term being analyzed */
  Index *pProbe,                  /* An index on pSrc */
  WhereCost 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 */
................................................................................
  Bitmask saved_prereq;           /* Original value of pNew->prereq */
  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
  int saved_nEq;                  /* Original value of pNew->u.btree.nEq */
  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */
  WhereCost saved_nOut;           /* Original value of pNew->nOut */
  int iCol;                       /* Index of the column in the table */
  int rc = SQLITE_OK;             /* Return code */
  WhereCost nRowEst;              /* Estimated index selectivity */
  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 );
................................................................................
  }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 = whereCostFromInt(pProbe->aiRowEst[pNew->u.btree.nEq+1]);
  }else{
    iCol = -1;
    nRowEst = 0;
  }
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  saved_nEq = pNew->u.btree.nEq;
  saved_nLTerm = pNew->nLTerm;
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = 0;
  rLogSize = estLog(whereCostFromInt(pProbe->aiRowEst[0]));
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 0;
    if( pTerm->prereqRight & pNew->maskSelf ) continue;
    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize;
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
      pNew->wsFlags |= WHERE_COLUMN_IN;
      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
        /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
        nIn = 46;  /* whereCostFromInt(25) */
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = whereCostFromInt(pExpr->x.pList->nExpr);
      }
      pNew->rRun += nIn;
      pNew->u.btree.nEq++;
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_EQ) ){
      assert( (pNew->wsFlags & (WHERE_COLUMN_NULL|WHERE_COLUMN_IN))!=0
                  || nInMul==0 );
      pNew->wsFlags |= WHERE_COLUMN_EQ;
      if( iCol<0  
       || (pProbe->onError!=OE_None && nInMul==0
           && pNew->u.btree.nEq==pProbe->nColumn-1)
      ){
        testcase( pNew->wsFlags & WHERE_COLUMN_IN );
        pNew->wsFlags |= WHERE_ONEROW;
      }
      pNew->u.btree.nEq++;
      pNew->nOut = nRowEst + nInMul;
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;
      nIn = 10;  /* Assume IS NULL matches two rows */
      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;
................................................................................
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
      WhereCost rDiv;
      whereRangeScanEst(pParse, pProbe, pNew->u.btree.nEq,
                        pBtm, pTop, &rDiv);
      pNew->nOut = saved_nOut - rDiv;
    }
#ifdef SQLITE_ENABLE_STAT3
    if( pNew->u.btree.nEq==1 && pProbe->nSample ){
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        rc = whereEqualScanEst(pParse, pProbe, pTerm->pExpr->pRight, &nOut);

      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pTerm->pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pProbe, pTerm->pExpr->x.pList, &nOut);

      }

      pNew->nOut = whereCostFromInt(nOut);
    }
#endif
    if( pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK) ){
      /* Step cost for each output row */
      pNew->rRun = whereCostAdd(pNew->rRun, pNew->nOut);
    }else{
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun = rLogSize>90 ? 
                        whereCostAdd(pNew->rRun, pNew->nOut+rLogSize-90) :
                        pNew->rRun;
    }
    /* TBD: Adjust nOut for additional constraints */
    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->prereq = saved_prereq;
  pNew->u.btree.nEq = saved_nEq;
  pNew->wsFlags = saved_wsFlags;
  pNew->nOut = saved_nOut;
  pNew->nLTerm = saved_nLTerm;
................................................................................
  int 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 */
  WhereCost rSize;            /* number of rows in the table */
  WhereCost rLogSize;         /* Logarithm of the number of rows in the table */
  
  pNew = pBuilder->pNew;
  pWInfo = pBuilder->pWInfo;
  pTabList = pWInfo->pTabList;
  pSrc = pTabList->a + pNew->iTab;
  assert( !IsVirtual(pSrc->pTab) );

................................................................................
    if( pSrc->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 = whereCostFromInt(pSrc->pTab->nRowEst);
  rLogSize = estLog(rSize);

  /* Automatic indexes */
  if( !pBuilder->pBest
   && pTabList->nSrc>1
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0 
   && !pSrc->viaCoroutine
................................................................................
    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->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        assert( 43==whereCostFromInt(20) );
        pNew->rSetup = 43 + rLogSize + rSize;
        pNew->nOut = 33;  assert( 33==whereCostFromInt(10) );
        pNew->rRun = whereCostAdd(rLogSize,pNew->nOut);
        pNew->wsFlags = WHERE_TEMP_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }

  /* Loop over all indices
  */
  for(; rc==SQLITE_OK && pProbe; pProbe=pProbe->pNext, iSortIdx++){
    pNew->u.btree.nEq = 0;
    pNew->nLTerm = 0;
    pNew->iSortIdx = 0;
    pNew->rSetup = 0;
    pNew->prereq = mExtra;
    pNew->u.btree.pIndex = pProbe;
    b = indexMightHelpWithOrderBy(pBuilder, pProbe, pSrc->iCursor);
    if( pProbe->tnum<=0 ){
      /* Integer primary key index */
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      pNew->nOut = rSize;
      pNew->rRun = whereCostAdd(rSize,rLogSize) + 16 + b*4;
      rc = whereLoopInsert(pBuilder, pNew);
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsUsedByIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
................................................................................
       && pProbe->bUnordered==0
       && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
       && sqlite3GlobalConfig.bUseCis
       && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        pNew->nOut = rSize;
        pNew->rRun = whereCostAdd(rSize,rLogSize) + ((m==0 && b) ? 10 : 0);
        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }
    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;
  }
  return rc;
}
................................................................................
      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 = (u8)((pIdxInfo->nOrderBy!=0)
                                     && pIdxInfo->orderByConsumed);
      pNew->rSetup = 0;
      pNew->rRun = whereCostFromInt((tRowcnt)pIdxInfo->estimatedCost);
      pNew->nOut = 46;  assert( 46 == whereCostFromInt(25) );
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 0;
      }
    }
  }  
................................................................................
        sBest.rRun = 0;
        if( IsVirtual(pItem->pTab) ){
          rc = whereLoopAddVirtual(&sSubBuild, mExtra);
        }else{
          rc = whereLoopAddBtree(&sSubBuild, mExtra);
        }
        if( sBest.maskSelf==0 ) break;
        assert( sBest.rSetup==0 );
        rTotal = whereCostAdd(rTotal, sBest.rRun);
        nRow = whereCostAdd(nRow, sBest.nOut);
        prereq |= sBest.prereq;
      }
      assert( pNew->nLSlot>=1 );
      pNew->nLTerm = 1;
      pNew->aLTerm[0] = pTerm;
      pNew->wsFlags = WHERE_MULTI_OR;
      pNew->rSetup = 0;
      pNew->rRun = rTotal;
      pNew->nOut = nRow;
      pNew->prereq = prereq;
      memset(&pNew->u, 0, sizeof(pNew->u));
      rc = whereLoopInsert(pBuilder, pNew);
      whereLoopClear(pWInfo->pParse->db, &sBest);
    }
................................................................................
  Bitmask mPrior = 0;
  int iTab;
  SrcList *pTabList = pWInfo->pTabList;
  struct SrcList_item *pItem;
  sqlite3 *db = pWInfo->pParse->db;
  int nTabList = pWInfo->nLevel;
  int rc = SQLITE_OK;
  WhereLoop *pNew;

  /* Loop over the tables in the join, from left to right */
  pNew = pBuilder->pNew;
  whereLoopInit(pNew);
  for(iTab=0, pItem=pTabList->a; iTab<nTabList; iTab++, pItem++){
    pNew->iTab = iTab;
    pNew->maskSelf = getMask(&pWInfo->sMaskSet, pItem->iCursor);
    if( (pItem->jointype & (JT_LEFT|JT_CROSS))!=0 ){
      mExtra = mPrior;
    }
................................................................................
    if( rc==SQLITE_OK ){
      rc = whereLoopAddOr(pBuilder, mExtra);
    }
    mPrior |= pNew->maskSelf;
    if( rc || db->mallocFailed ) break;
  }
  whereLoopClear(db, pNew);

  return rc;
}

/*
** Examine a WherePath (with the addition of the extra WhereLoop of the 5th
** parameters) to see if it outputs rows in the requested ORDER BY
** (or GROUP BY) without requiring a separate source operation.  Return:
................................................................................
  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;
  }

  /* Seed the search with a single WherePath containing zero WhereLoops */
  aFrom[0].nRow = 0;
  nFrom = 1;

  /* Precompute the cost of sorting the final result set, if the caller
  ** to sqlite3WhereBegin() was concerned about sorting */
  rSortCost = 0;
  if( pWInfo->pOrderBy==0 || nRowEst==0 ){
    aFrom[0].isOrderedValid = 1;
  }else{
    /* Compute an estimate on the cost to sort the entire result set */
    rSortCost = nRowEst + estLog(nRowEst);
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      sqlite3DebugPrintf("---- sort cost=%-3d\n", rSortCost);
    }
#endif
  }

  /* 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 */
................................................................................
        Bitmask revMask = 0;
        u8 isOrderedValid = pFrom->isOrderedValid;
        u8 isOrdered = pFrom->isOrdered;
        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 */
        rCost = whereCostAdd(pWLoop->rSetup,pWLoop->rRun + pFrom->nRow);
        rCost = whereCostAdd(rCost, pFrom->rCost);
        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( !isOrderedValid ){
          switch( wherePathSatisfiesOrderBy(pWInfo, pFrom, iLoop, iLoop==nLoop-1,
                                            pWLoop, &revMask) ){
            case 1:  /* Yes.  pFrom+pWLoop does satisfy the ORDER BY clause */
              isOrdered = 1;
              isOrderedValid = 1;
              break;
            case 0:  /* No.  pFrom+pWLoop will require a separate sort */
              isOrdered = 0;
              isOrderedValid = 1;
              rCost = whereCostAdd(rCost, rSortCost);
              break;
            default: /* Cannot tell yet.  Try again on the next iteration */
              break;
          }
        }else{
          revMask = pFrom->revLoop;
        }
................................................................................
            break;
          }
        }
        if( jj>=nTo ){
          if( nTo>=mxChoice && rCost>=mxCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf("Skip   %s cost=%3d order=%c\n",
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
            }
#endif
            continue;
          }
          /* Add a new Path to the aTo[] set */
................................................................................
          }else{
            /* New path replaces the prior worst to keep count below mxChoice */
            for(jj=nTo-1; aTo[jj].rCost<mxCost; jj--){ assert(jj>0); }
          }
          pTo = &aTo[jj];
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf("New    %s cost=%-3d order=%c\n",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
          }
#endif
        }else{
          if( pTo->rCost<=rCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf(
                  "Skip   %s cost=%-3d order=%c",
                  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') : '?');
            sqlite3DebugPrintf("  was %s cost=%-3d order=%c\n",
                wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : '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 = pFrom->nRow + pWLoop->nOut;
        pTo->rCost = rCost;
        pTo->isOrderedValid = isOrderedValid;
        pTo->isOrdered = isOrdered;
        memcpy(pTo->aLoop, pFrom->aLoop, sizeof(WhereLoop*)*iLoop);
        pTo->aLoop[iLoop] = pWLoop;
        if( nTo>=mxChoice ){
          mxCost = aTo[0].rCost;
................................................................................
      }
    }

#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      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->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
        if( pTo->isOrderedValid && pTo->isOrdered ){
          sqlite3DebugPrintf(" rev=0x%llx\n", pTo->revLoop);
        }else{
          sqlite3DebugPrintf("\n");
        }
................................................................................
** 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;
................................................................................
  pLoop->wsFlags = 0;
  pTerm = findTerm(pWC, iCur, -1, 0, WO_EQ, 0);
  if( pTerm ){
    pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_IPK|WHERE_ONEROW;
    pLoop->aLTerm[0] = pTerm;
    pLoop->nLTerm = 1;
    pLoop->u.btree.nEq = 1;
    pLoop->rRun = 33;  /* 33 == whereCostFromInt(10) */
  }else{
    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
      if( pIdx->onError==OE_None ) continue;
      for(j=0; j<pIdx->nColumn; j++){
        pTerm = findTerm(pWC, iCur, pIdx->aiColumn[j], 0, WO_EQ, pIdx);
        if( pTerm==0 ) break;
        whereLoopResize(pWInfo->pParse->db, pLoop, j);
................................................................................
      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;
      if( (pItem->colUsed & ~columnsUsedByIndex(pIdx))==0 ){
        pLoop->wsFlags |= WHERE_IDX_ONLY;
      }
      pLoop->nLTerm = j;
      pLoop->u.btree.nEq = j;
      pLoop->u.btree.pIndex = pIdx;
      pLoop->rRun = 39;  /* 39 == whereCostFromInt(15) */
      break;
    }
  }
  if( pLoop->wsFlags ){
    pLoop->nOut = (WhereCost)1;
    pWInfo->a[0].pWLoop = pLoop;
    pLoop->maskSelf = getMask(&pWInfo->sMaskSet, iCur);
................................................................................
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = &pWInfo->sMaskSet;
  sWLB.pWInfo = pWInfo;
  sWLB.pWC = &pWInfo->sWC;
  sWLB.pNew = (WhereLoop*)&pWInfo->a[nTabList];
  whereLoopInit(sWLB.pNew);
#ifdef SQLITE_DEBUG
  sWLB.pNew->cId = '*';
#endif

  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via
  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */
  if( OptimizationDisabled(db, SQLITE_DistinctOpt) ) pDistinct = 0;

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
................................................................................
  if( pDistinct && isDistinctRedundant(pParse,pTabList,&pWInfo->sWC,pDistinct) ){
    pDistinct = 0;
    pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
  }

  /* Construct the WhereLoop objects */
  WHERETRACE(("*** Optimizer Start ***\n"));
  if( nTabList!=1 || whereShortCut(&sWLB)==0 ){
    rc = whereLoopAddAll(&sWLB);
    if( rc ) goto whereBeginError;
  
    /* Display all of the WhereLoop objects if wheretrace is enabled */
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace ){
      WhereLoop *p;