SQLite

      Expr *pCExpr = sqlite3ExprSkipCollate(pList->a[0].pExpr);
      sqlite3RenameTokenRemap(pParse, &pTab->iPKey, pCExpr);
    }
    pTab->iPKey = iCol;
    pTab->keyConf = (u8)onError;
    assert( autoInc==0 || autoInc==1 );
    pTab->tabFlags |= autoInc*TF_Autoincrement;
    if( pList ) pParse->iPkSortOrder = pList->a[0].sortFlags;
  }else if( autoInc ){
#ifndef SQLITE_OMIT_AUTOINCREMENT
    sqlite3ErrorMsg(pParse, "AUTOINCREMENT is only allowed on an "
       "INTEGER PRIMARY KEY");
#endif
  }else{
    sqlite3CreateIndex(pParse, 0, 0, 0, pList, onError, 0,

    sqlite3TokenInit(&ipkToken, pTab->aCol[pTab->iPKey].zName);
    pList = sqlite3ExprListAppend(pParse, 0, 
                  sqlite3ExprAlloc(db, TK_ID, &ipkToken, 0));
    if( pList==0 ) return;
    if( IN_RENAME_OBJECT ){
      sqlite3RenameTokenRemap(pParse, pList->a[0].pExpr, &pTab->iPKey);
    }
    pList->a[0].sortFlags = pParse->iPkSortOrder;
    assert( pParse->pNewTable==pTab );
    pTab->iPKey = -1;
    sqlite3CreateIndex(pParse, 0, 0, 0, pList, pTab->keyConf, 0, 0, 0, 0,
                       SQLITE_IDXTYPE_PRIMARYKEY);
    if( db->mallocFailed || pParse->nErr ) return;
    pPk = sqlite3PrimaryKeyIndex(pTab);
    assert( pPk->nKeyCol==1 );

    Column *pCol = &pTab->aCol[pTab->nCol-1];
    pCol->colFlags |= COLFLAG_UNIQUE;
    sqlite3TokenInit(&prevCol, pCol->zName);
    pList = sqlite3ExprListAppend(pParse, 0,
              sqlite3ExprAlloc(db, TK_ID, &prevCol, 0));
    if( pList==0 ) goto exit_create_index;
    assert( pList->nExpr==1 );
    sqlite3ExprListSetSortOrder(pList, sortOrder, 0);
  }else{
    sqlite3ExprListCheckLength(pParse, pList, "index");
    if( pParse->nErr ) goto exit_create_index;
  }

  /* Figure out how many bytes of space are required to store explicitly
  ** specified collation sequence names.

      zColl = pTab->aCol[j].zColl;
    }
    if( !zColl ) zColl = sqlite3StrBINARY;
    if( !db->init.busy && !sqlite3LocateCollSeq(pParse, zColl) ){
      goto exit_create_index;
    }
    pIndex->azColl[i] = zColl;
    requestedSortOrder = pListItem->sortFlags & sortOrderMask;
    pIndex->aSortOrder[i] = (u8)requestedSortOrder;
  }

  /* Append the table key to the end of the index.  For WITHOUT ROWID
  ** tables (when pPk!=0) this will be the declared PRIMARY KEY.  For
  ** normal tables (when pPk==0) this will be the rowid.
  */

  }
  if( pKey ){
    assert( sqlite3KeyInfoIsWriteable(pKey) );
    for(i=0; i<nCol; i++){
      const char *zColl = pIdx->azColl[i];
      pKey->aColl[i] = zColl==sqlite3StrBINARY ? 0 :
                        sqlite3LocateCollSeq(pParse, zColl);
      pKey->aSortFlags[i] = pIdx->aSortOrder[i];
      assert( 0==(pKey->aSortFlags[i] & KEYINFO_ORDER_BIGNULL) );
    }
    if( pParse->nErr ){
      assert( pParse->rc==SQLITE_ERROR_MISSING_COLLSEQ );
      if( pIdx->bNoQuery==0 ){
        /* Deactivate the index because it contains an unknown collating
        ** sequence.  The only way to reactive the index is to reload the
        ** schema.  Adding the missing collating sequence later does not

        assert( pNewExpr->iColumn==pItem[-1].pExpr->iColumn+1 );
        assert( pPriorSelectCol==pItem[-1].pExpr->pLeft );
        pNewExpr->pLeft = pPriorSelectCol;
      }
    }
    pItem->zName = sqlite3DbStrDup(db, pOldItem->zName);
    pItem->zSpan = sqlite3DbStrDup(db, pOldItem->zSpan);
    pItem->sortFlags = pOldItem->sortFlags;
    pItem->done = 0;
    pItem->bSpanIsTab = pOldItem->bSpanIsTab;
    pItem->bSorterRef = pOldItem->bSorterRef;
    pItem->u = pOldItem->u;
  }
  return pNew;
}

  sqlite3IdListDelete(db, pColumns);
  return pList;
}

/*
** Set the sort order for the last element on the given ExprList.
*/
void sqlite3ExprListSetSortOrder(ExprList *p, int iSortOrder, int eNulls){
  if( p==0 ) return;
  assert( p->nExpr>0 );

  assert( SQLITE_SO_UNDEFINED<0 && SQLITE_SO_ASC==0 && SQLITE_SO_DESC>0 );
  assert( iSortOrder==SQLITE_SO_UNDEFINED 
       || iSortOrder==SQLITE_SO_ASC 
       || iSortOrder==SQLITE_SO_DESC 

  );
  assert( eNulls==SQLITE_SO_UNDEFINED 
       || eNulls==SQLITE_SO_ASC 
       || eNulls==SQLITE_SO_DESC 
  );

  if( iSortOrder==SQLITE_SO_UNDEFINED ) iSortOrder = SQLITE_SO_ASC;
  p->a[p->nExpr-1].sortFlags = (u8)iSortOrder;
  if( eNulls!=SQLITE_SO_UNDEFINED && iSortOrder!=eNulls ){
    p->a[p->nExpr-1].sortFlags |= KEYINFO_ORDER_BIGNULL;
  }
}

/*
** Set the ExprList.a[].zName element of the most recently added item
** on the expression list.
**
** pList might be NULL following an OOM error.  But pName should never be

  int i;
  if( pA==0 && pB==0 ) return 0;
  if( pA==0 || pB==0 ) return 1;
  if( pA->nExpr!=pB->nExpr ) return 1;
  for(i=0; i<pA->nExpr; i++){
    Expr *pExprA = pA->a[i].pExpr;
    Expr *pExprB = pB->a[i].pExpr;
    if( pA->a[i].sortFlags!=pB->a[i].sortFlags ) return 1;
    if( sqlite3ExprCompare(0, pExprA, pExprB, iTab) ) return 1;
  }
  return 0;
}

/*
** Like sqlite3ExprCompare() except COLLATE operators at the top-level

%fallback ID
  ABORT ACTION AFTER ANALYZE ASC ATTACH BEFORE BEGIN BY CASCADE CAST COLUMNKW
  CONFLICT DATABASE DEFERRED DESC DETACH DO
  EACH END EXCLUSIVE EXPLAIN FAIL FOR
  IGNORE IMMEDIATE INITIALLY INSTEAD LIKE_KW MATCH NO PLAN
  QUERY KEY OF OFFSET PRAGMA RAISE RECURSIVE RELEASE REPLACE RESTRICT ROW ROWS
  ROLLBACK SAVEPOINT TEMP TRIGGER VACUUM VIEW VIRTUAL WITH WITHOUT
  NULLS FIRST LAST
%ifdef SQLITE_OMIT_COMPOUND_SELECT
  EXCEPT INTERSECT UNION
%endif SQLITE_OMIT_COMPOUND_SELECT
%ifndef SQLITE_OMIT_WINDOWFUNC
  CURRENT FOLLOWING PARTITION PRECEDING RANGE UNBOUNDED
  EXCLUDE GROUPS OTHERS TIES
%endif SQLITE_OMIT_WINDOWFUNC

// sort order.
//
%type sortlist {ExprList*}
%destructor sortlist {sqlite3ExprListDelete(pParse->db, $$);}

orderby_opt(A) ::= .                          {A = 0;}
orderby_opt(A) ::= ORDER BY sortlist(X).      {A = X;}
sortlist(A) ::= sortlist(A) COMMA expr(Y) sortorder(Z) nulls(X). {
  A = sqlite3ExprListAppend(pParse,A,Y);
  sqlite3ExprListSetSortOrder(A,Z,X);
}
sortlist(A) ::= expr(Y) sortorder(Z) nulls(X). {
  A = sqlite3ExprListAppend(pParse,0,Y); /*A-overwrites-Y*/
  sqlite3ExprListSetSortOrder(A,Z,X);
}

%type sortorder {int}

sortorder(A) ::= ASC.           {A = SQLITE_SO_ASC;}
sortorder(A) ::= DESC.          {A = SQLITE_SO_DESC;}
sortorder(A) ::= .              {A = SQLITE_SO_UNDEFINED;}

%type nulls {int}
nulls(A) ::= NULLS FIRST.       {A = SQLITE_SO_ASC;}
nulls(A) ::= NULLS LAST.        {A = SQLITE_SO_DESC;}
nulls(A) ::= .                  {A = SQLITE_SO_UNDEFINED;}

%type groupby_opt {ExprList*}
%destructor groupby_opt {sqlite3ExprListDelete(pParse->db, $$);}
groupby_opt(A) ::= .                      {A = 0;}
groupby_opt(A) ::= GROUP BY nexprlist(X). {A = X;}

%type having_opt {Expr*}
%destructor having_opt {sqlite3ExprDelete(pParse->db, $$);}

    }
    VdbeCoverage(v);
    sqlite3VdbeAddOp3(v, OP_Compare, regPrevKey, regBase, pSort->nOBSat);
    pOp = sqlite3VdbeGetOp(v, pSort->addrSortIndex);
    if( pParse->db->mallocFailed ) return;
    pOp->p2 = nKey + nData;
    pKI = pOp->p4.pKeyInfo;
    memset(pKI->aSortFlags, 0, pKI->nKeyField); /* Makes OP_Jump testable */
    sqlite3VdbeChangeP4(v, -1, (char*)pKI, P4_KEYINFO);
    testcase( pKI->nAllField > pKI->nKeyField+2 );
    pOp->p4.pKeyInfo = sqlite3KeyInfoFromExprList(pParse,pSort->pOrderBy,nOBSat,
                                           pKI->nAllField-pKI->nKeyField-1);
    addrJmp = sqlite3VdbeCurrentAddr(v);
    sqlite3VdbeAddOp3(v, OP_Jump, addrJmp+1, 0, addrJmp+1); VdbeCoverage(v);
    pSort->labelBkOut = sqlite3VdbeMakeLabel(pParse);

** Allocate a KeyInfo object sufficient for an index of N key columns and
** X extra columns.
*/
KeyInfo *sqlite3KeyInfoAlloc(sqlite3 *db, int N, int X){
  int nExtra = (N+X)*(sizeof(CollSeq*)+1) - sizeof(CollSeq*);
  KeyInfo *p = sqlite3DbMallocRawNN(db, sizeof(KeyInfo) + nExtra);
  if( p ){
    p->aSortFlags = (u8*)&p->aColl[N+X];
    p->nKeyField = (u16)N;
    p->nAllField = (u16)(N+X);
    p->enc = ENC(db);
    p->db = db;
    p->nRef = 1;
    memset(&p[1], 0, nExtra);
  }else{

  nExpr = pList->nExpr;
  pInfo = sqlite3KeyInfoAlloc(db, nExpr-iStart, nExtra+1);
  if( pInfo ){
    assert( sqlite3KeyInfoIsWriteable(pInfo) );
    for(i=iStart, pItem=pList->a+iStart; i<nExpr; i++, pItem++){
      pInfo->aColl[i-iStart] = sqlite3ExprNNCollSeq(pParse, pItem->pExpr);
      pInfo->aSortFlags[i-iStart] = pItem->sortFlags;
    }
  }
  return pInfo;
}

/*
** Name of the connection operator, used for error messages.

        pColl = multiSelectCollSeq(pParse, p, pItem->u.x.iOrderByCol-1);
        if( pColl==0 ) pColl = db->pDfltColl;
        pOrderBy->a[i].pExpr =
          sqlite3ExprAddCollateString(pParse, pTerm, pColl->zName);
      }
      assert( sqlite3KeyInfoIsWriteable(pRet) );
      pRet->aColl[i] = pColl;
      pRet->aSortFlags[i] = pOrderBy->a[i].sortFlags;
    }
  }

  return pRet;
}

#ifndef SQLITE_OMIT_CTE

    pParse->nMem += nExpr+1;
    sqlite3VdbeAddOp2(v, OP_Integer, 0, regPrev);
    pKeyDup = sqlite3KeyInfoAlloc(db, nExpr, 1);
    if( pKeyDup ){
      assert( sqlite3KeyInfoIsWriteable(pKeyDup) );
      for(i=0; i<nExpr; i++){
        pKeyDup->aColl[i] = multiSelectCollSeq(pParse, p, i);
        pKeyDup->aSortFlags[i] = 0;
      }
    }
  }
 
  /* Separate the left and the right query from one another
  */
  p->pPrior = 0;

    eRet = WHERE_ORDERBY_MAX;
    sortOrder = SQLITE_SO_DESC;
  }else{
    return eRet;
  }
  *ppMinMax = pOrderBy = sqlite3ExprListDup(db, pEList, 0);
  assert( pOrderBy!=0 || db->mallocFailed );
  if( pOrderBy ) pOrderBy->a[0].sortFlags = sortOrder;
  return eRet;
}

/*
** The select statement passed as the first argument is an aggregate query.
** The second argument is the associated aggregate-info object. This 
** function tests if the SELECT is of the form:

*/
struct KeyInfo {
  u32 nRef;           /* Number of references to this KeyInfo object */
  u8 enc;             /* Text encoding - one of the SQLITE_UTF* values */
  u16 nKeyField;      /* Number of key columns in the index */
  u16 nAllField;      /* Total columns, including key plus others */
  sqlite3 *db;        /* The database connection */
  u8 *aSortFlags;     /* Sort order for each column. */
  CollSeq *aColl[1];  /* Collating sequence for each term of the key */
};

#define KEYINFO_ORDER_DESC    0x01
#define KEYINFO_ORDER_BIGNULL 0x02

/*
** This object holds a record which has been parsed out into individual
** fields, for the purposes of doing a comparison.
**
** A record is an object that contains one or more fields of data.
** Records are used to store the content of a table row and to store

*/
struct ExprList {
  int nExpr;             /* Number of expressions on the list */
  struct ExprList_item { /* For each expression in the list */
    Expr *pExpr;            /* The parse tree for this expression */
    char *zName;            /* Token associated with this expression */
    char *zSpan;            /* Original text of the expression */
    u8 sortFlags;           /* 1 for DESC or 0 for ASC */
    unsigned done :1;       /* A flag to indicate when processing is finished */
    unsigned bSpanIsTab :1; /* zSpan holds DB.TABLE.COLUMN */
    unsigned reusable :1;   /* Constant expression is reusable */
    unsigned bSorterRef :1; /* Defer evaluation until after sorting */
    union {
      struct {
        u16 iOrderByCol;      /* For ORDER BY, column number in result set */

Expr *sqlite3ExprSimplifiedAndOr(Expr*);
Expr *sqlite3ExprFunction(Parse*,ExprList*, Token*, int);
void sqlite3ExprAssignVarNumber(Parse*, Expr*, u32);
void sqlite3ExprDelete(sqlite3*, Expr*);
void sqlite3ExprUnmapAndDelete(Parse*, Expr*);
ExprList *sqlite3ExprListAppend(Parse*,ExprList*,Expr*);
ExprList *sqlite3ExprListAppendVector(Parse*,ExprList*,IdList*,Expr*);
void sqlite3ExprListSetSortOrder(ExprList*,int,int);
void sqlite3ExprListSetName(Parse*,ExprList*,Token*,int);
void sqlite3ExprListSetSpan(Parse*,ExprList*,const char*,const char*);
void sqlite3ExprListDelete(sqlite3*, ExprList*);
u32 sqlite3ExprListFlags(const ExprList*);
int sqlite3IndexHasDuplicateRootPage(Index*);
int sqlite3Init(sqlite3*, char**);
int sqlite3InitCallback(void*, int, char**, char**);

    idx = aPermute ? aPermute[i] : i;
    assert( memIsValid(&aMem[p1+idx]) );
    assert( memIsValid(&aMem[p2+idx]) );
    REGISTER_TRACE(p1+idx, &aMem[p1+idx]);
    REGISTER_TRACE(p2+idx, &aMem[p2+idx]);
    assert( i<pKeyInfo->nKeyField );
    pColl = pKeyInfo->aColl[i];
    bRev = (pKeyInfo->aSortFlags[i] & KEYINFO_ORDER_DESC);
    iCompare = sqlite3MemCompare(&aMem[p1+idx], &aMem[p2+idx], pColl);
    if( iCompare ){
      if( (pKeyInfo->aSortFlags[i] & KEYINFO_ORDER_BIGNULL) 
       && ((aMem[p1+idx].flags & MEM_Null) || (aMem[p2+idx].flags & MEM_Null))
      ){
        iCompare = -iCompare;
      }
      if( bRev ) iCompare = -iCompare;
      break;
    }
  }
  break;
}

  StrAccum x;
  assert( nTemp>=20 );
  sqlite3StrAccumInit(&x, 0, zTemp, nTemp, 0);
  switch( pOp->p4type ){
    case P4_KEYINFO: {
      int j;
      KeyInfo *pKeyInfo = pOp->p4.pKeyInfo;
      assert( pKeyInfo->aSortFlags!=0 );
      sqlite3_str_appendf(&x, "k(%d", pKeyInfo->nKeyField);
      for(j=0; j<pKeyInfo->nKeyField; j++){
        CollSeq *pColl = pKeyInfo->aColl[j];
        const char *zColl = pColl ? pColl->zName : "";
        if( strcmp(zColl, "BINARY")==0 ) zColl = "B";
        sqlite3_str_appendf(&x, ",%s%s%s", 
               (pKeyInfo->aSortFlags[j] & KEYINFO_ORDER_DESC) ? "-" : "", 
               (pKeyInfo->aSortFlags[j] & KEYINFO_ORDER_BIGNULL)? "N." : "", 
               zColl);
      }
      sqlite3_str_append(&x, ")", 1);
      break;
    }
#ifdef SQLITE_ENABLE_CURSOR_HINTS
    case P4_EXPR: {
      displayP4Expr(&x, pOp->p4.pExpr);

){
  UnpackedRecord *p;              /* Unpacked record to return */
  int nByte;                      /* Number of bytes required for *p */
  nByte = ROUND8(sizeof(UnpackedRecord)) + sizeof(Mem)*(pKeyInfo->nKeyField+1);
  p = (UnpackedRecord *)sqlite3DbMallocRaw(pKeyInfo->db, nByte);
  if( !p ) return 0;
  p->aMem = (Mem*)&((char*)p)[ROUND8(sizeof(UnpackedRecord))];
  assert( pKeyInfo->aSortFlags!=0 );
  p->pKeyInfo = pKeyInfo;
  p->nField = pKeyInfo->nKeyField + 1;
  return p;
}

/*
** Given the nKey-byte encoding of a record in pKey[], populate the 

  */
  /*  mem1.u.i = 0;  // not needed, here to silence compiler warning */
  
  idx1 = getVarint32(aKey1, szHdr1);
  if( szHdr1>98307 ) return SQLITE_CORRUPT;
  d1 = szHdr1;
  assert( pKeyInfo->nAllField>=pPKey2->nField || CORRUPT_DB );
  assert( pKeyInfo->aSortFlags!=0 );
  assert( pKeyInfo->nKeyField>0 );
  assert( idx1<=szHdr1 || CORRUPT_DB );
  do{
    u32 serial_type1;

    /* Read the serial types for the next element in each key. */
    idx1 += getVarint32( aKey1+idx1, serial_type1 );

    /* Do the comparison
    */
    rc = sqlite3MemCompare(&mem1, &pPKey2->aMem[i],
                           pKeyInfo->nAllField>i ? pKeyInfo->aColl[i] : 0);
    if( rc!=0 ){
      assert( mem1.szMalloc==0 );  /* See comment below */
      if( (pKeyInfo->aSortFlags[i] & KEYINFO_ORDER_BIGNULL)
       && ((mem1.flags & MEM_Null) || (pPKey2->aMem[i].flags & MEM_Null)) 
      ){
        rc = -rc;
      }
      if( pKeyInfo->aSortFlags[i] & KEYINFO_ORDER_DESC ){
        rc = -rc;  /* Invert the result for DESC sort order. */
      }
      goto debugCompareEnd;
    }
    i++;
  }while( idx1<szHdr1 && i<pPKey2->nField );

    pPKey2->errCode = (u8)SQLITE_CORRUPT_BKPT;
    return 0;  /* Corruption */
  }

  VVA_ONLY( mem1.szMalloc = 0; ) /* Only needed by assert() statements */
  assert( pPKey2->pKeyInfo->nAllField>=pPKey2->nField 
       || CORRUPT_DB );
  assert( pPKey2->pKeyInfo->aSortFlags!=0 );
  assert( pPKey2->pKeyInfo->nKeyField>0 );
  assert( idx1<=szHdr1 || CORRUPT_DB );
  do{
    u32 serial_type;

    /* RHS is an integer */
    if( pRhs->flags & (MEM_Int|MEM_IntReal) ){

    /* RHS is null */
    else{
      serial_type = aKey1[idx1];
      rc = (serial_type!=0);
    }

    if( rc!=0 ){
      int sortFlags = pPKey2->pKeyInfo->aSortFlags[i];
      if( sortFlags ){
        if( (sortFlags & KEYINFO_ORDER_BIGNULL)==0
         || ((sortFlags & KEYINFO_ORDER_DESC)
           !=(serial_type==0 || (pRhs->flags&MEM_Null)))
        ){
          rc = -rc;
        }
      }
      assert( vdbeRecordCompareDebug(nKey1, pKey1, pPKey2, rc) );
      assert( mem1.szMalloc==0 );  /* See comment below */
      return rc;
    }

    i++;

  ** is an integer.
  **
  ** The easiest way to enforce this limit is to consider only records with
  ** 13 fields or less. If the first field is an integer, the maximum legal
  ** header size is (12*5 + 1 + 1) bytes.  */
  if( p->pKeyInfo->nAllField<=13 ){
    int flags = p->aMem[0].flags;
    if( p->pKeyInfo->aSortFlags[0] ){
      if( p->pKeyInfo->aSortFlags[0] & KEYINFO_ORDER_BIGNULL ){
        return sqlite3VdbeRecordCompare;
      }
      p->r1 = 1;
      p->r2 = -1;
    }else{
      p->r1 = -1;
      p->r2 = 1;
    }
    if( (flags & MEM_Int) ){

  if( res==0 ){
    if( pTask->pSorter->pKeyInfo->nKeyField>1 ){
      res = vdbeSorterCompareTail(
          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2
      );
    }
  }else{
    assert( !(pTask->pSorter->pKeyInfo->aSortFlags[0]&KEYINFO_ORDER_BIGNULL) );
    if( pTask->pSorter->pKeyInfo->aSortFlags[0] ){
      res = res * -1;
    }
  }

  return res;
}

  if( res==0 ){
    if( pTask->pSorter->pKeyInfo->nKeyField>1 ){
      res = vdbeSorterCompareTail(
          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2
      );
    }
  }else if( pTask->pSorter->pKeyInfo->aSortFlags[0] ){
    assert( !(pTask->pSorter->pKeyInfo->aSortFlags[0]&KEYINFO_ORDER_BIGNULL) );
    res = res * -1;
  }

  return res;
}

/*

        pSorter->list.aMemory = (u8*)sqlite3Malloc(pgsz);
        if( !pSorter->list.aMemory ) rc = SQLITE_NOMEM_BKPT;
      }
    }

    if( pKeyInfo->nAllField<13 
     && (pKeyInfo->aColl[0]==0 || pKeyInfo->aColl[0]==db->pDfltColl)
     && (pKeyInfo->aSortFlags[0] & KEYINFO_ORDER_BIGNULL)==0
    ){
      pSorter->typeMask = SORTER_TYPE_INTEGER | SORTER_TYPE_TEXT;
    }
  }

  return rc;
}

    }

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

  *pmNoOmit = mNoOmit;
  return pIdxInfo;
}

/*

            if( pOBExpr->iColumn!=iColumn ) continue;
          }else{
            Expr *pIdxExpr = pIndex->aColExpr->a[j].pExpr;
            if( sqlite3ExprCompareSkip(pOBExpr, pIdxExpr, iCur) ){
              continue;
            }
          }
          if( pOrderBy->a[i].sortFlags & KEYINFO_ORDER_BIGNULL ) continue;
          if( iColumn!=XN_ROWID ){
            pColl = sqlite3ExprNNCollSeq(pWInfo->pParse, pOrderBy->a[i].pExpr);
            if( sqlite3StrICmp(pColl->zName, pIndex->azColl[j])!=0 ) continue;
          }
          if( wctrlFlags & WHERE_DISTINCTBY ){
            pLoop->u.btree.nDistinctCol = j+1;
          }
          isMatch = 1;
          break;
        }
        if( isMatch && (wctrlFlags & WHERE_GROUPBY)==0 ){
          /* Make sure the sort order is compatible in an ORDER BY clause.
          ** Sort order is irrelevant for a GROUP BY clause. */
          assert( (pOrderBy->a[i].sortFlags & KEYINFO_ORDER_BIGNULL)==0 );
          if( revSet ){
            if( (rev ^ revIdx)!=pOrderBy->a[i].sortFlags ) isMatch = 0;
          }else{
            rev = revIdx ^ pOrderBy->a[i].sortFlags;
            if( rev ) *pRevMask |= MASKBIT(iLoop);
            revSet = 1;
          }
        }
        if( isMatch ){
          if( iColumn==XN_ROWID ){
            testcase( distinctColumns==0 );

    for(i=0; i<pAppend->nExpr; i++){
      Expr *pDup = sqlite3ExprDup(pParse->db, pAppend->a[i].pExpr, 0);
      if( bIntToNull && pDup && pDup->op==TK_INTEGER ){
        pDup->op = TK_NULL;
        pDup->flags &= ~(EP_IntValue|EP_IsTrue|EP_IsFalse);
      }
      pList = sqlite3ExprListAppend(pParse, pList, pDup);
      if( pList ) pList->a[nInit+i].sortFlags = pAppend->a[i].sortFlags;
    }
  }
  return pList;
}

/*
** If the SELECT statement passed as the second argument does not invoke

      */
      ExprList *pList = pWin->pOwner->x.pList;
      KeyInfo *pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pList, 0, 0);
      pWin->csrApp = pParse->nTab++;
      pWin->regApp = pParse->nMem+1;
      pParse->nMem += 3;
      if( pKeyInfo && pWin->pFunc->zName[1]=='i' ){
        assert( pKeyInfo->aSortFlags[0]==0 );
        pKeyInfo->aSortFlags[0] = KEYINFO_ORDER_DESC;
      }
      sqlite3VdbeAddOp2(v, OP_OpenEphemeral, pWin->csrApp, 2);
      sqlite3VdbeAppendP4(v, pKeyInfo, P4_KEYINFO);
      sqlite3VdbeAddOp2(v, OP_Integer, 0, pWin->regApp+1);
    }
    else if( p->zName==nth_valueName || p->zName==first_valueName ){
      /* Allocate two registers at pWin->regApp. These will be used to

  int arith = OP_Add;
  int addrGe;

  int regString = ++pParse->nMem;

  assert( op==OP_Ge || op==OP_Gt || op==OP_Le );
  assert( p->pMWin->pOrderBy && p->pMWin->pOrderBy->nExpr==1 );
  if( p->pMWin->pOrderBy->a[0].sortFlags & KEYINFO_ORDER_DESC ){
    switch( op ){
      case OP_Ge: op = OP_Le; break;
      case OP_Gt: op = OP_Lt; break;
      default: assert( op==OP_Le ); op = OP_Ge; break;
    }
    arith = OP_Subtract;
  }

# 2019 August 10
#
# The author disclaims copyright to this source code.  In place of
# a legal notice, here is a blessing:
#
#    May you do good and not evil.
#    May you find forgiveness for yourself and forgive others.
#    May you share freely, never taking more than you give.
#
#***********************************************************************
# This file implements regression tests for SQLite library.
#

####################################################
# DO NOT EDIT! THIS FILE IS AUTOMATICALLY GENERATED!
####################################################

set testdir [file dirname $argv0]
source $testdir/tester.tcl
set testprefix nulls1

do_execsql_test 1.0 {
  DROP TABLE IF EXISTS t3;
  CREATE TABLE t3(a INTEGER);
  INSERT INTO t3 VALUES(NULL), (10), (30), (20), (NULL);
} {}

for {set a 0} {$a < 2} {incr a} {
  foreach {tn limit} {
    1 ""
    2 "LIMIT 10"
  } {
    do_execsql_test 1.$a.$tn.1 "
      SELECT a FROM t3 ORDER BY a nULLS FIRST $limit
    " {{}   {}   10   20   30}
    
    do_execsql_test 1.$a.$tn.2 "
      SELECT a FROM t3 ORDER BY a nULLS LAST $limit
    " {10   20   30   {}   {}}
    
    do_execsql_test 1.$a.$tn.3 "
      SELECT a FROM t3 ORDER BY a DESC nULLS FIRST $limit
    " {{}   {}   30   20   10}
    
    do_execsql_test 1.$a.$tn.4 "
      SELECT a FROM t3 ORDER BY a DESC nULLS LAST $limit
    " {30   20   10   {}   {}}
  }

  catchsql { CREATE INDEX i1 ON t3(a) }
}

finish_test

  { "EXCEPT",           "TK_EXCEPT",       COMPOUND               },
  { "EXCLUSIVE",        "TK_EXCLUSIVE",    ALWAYS                 },
  { "EXCLUDE",          "TK_EXCLUDE",      WINDOWFUNC             },
  { "EXISTS",           "TK_EXISTS",       ALWAYS                 },
  { "EXPLAIN",          "TK_EXPLAIN",      EXPLAIN                },
  { "FAIL",             "TK_FAIL",         CONFLICT|TRIGGER       },
  { "FILTER",           "TK_FILTER",       WINDOWFUNC             },
  { "FIRST",            "TK_FIRST",        ALWAYS                 },
  { "FOLLOWING",        "TK_FOLLOWING",    WINDOWFUNC             },
  { "FOR",              "TK_FOR",          TRIGGER                },
  { "FOREIGN",          "TK_FOREIGN",      FKEY                   },
  { "FROM",             "TK_FROM",         ALWAYS                 },
  { "FULL",             "TK_JOIN_KW",      ALWAYS                 },
  { "GLOB",             "TK_LIKE_KW",      ALWAYS                 },
  { "GROUP",            "TK_GROUP",        ALWAYS                 },

  { "INSTEAD",          "TK_INSTEAD",      TRIGGER                },
  { "INTERSECT",        "TK_INTERSECT",    COMPOUND               },
  { "INTO",             "TK_INTO",         ALWAYS                 },
  { "IS",               "TK_IS",           ALWAYS                 },
  { "ISNULL",           "TK_ISNULL",       ALWAYS                 },
  { "JOIN",             "TK_JOIN",         ALWAYS                 },
  { "KEY",              "TK_KEY",          ALWAYS                 },
  { "LAST",             "TK_LAST",         ALWAYS                 },
  { "LEFT",             "TK_JOIN_KW",      ALWAYS                 },
  { "LIKE",             "TK_LIKE_KW",      ALWAYS                 },
  { "LIMIT",            "TK_LIMIT",        ALWAYS                 },
  { "MATCH",            "TK_MATCH",        ALWAYS                 },
  { "NATURAL",          "TK_JOIN_KW",      ALWAYS                 },
  { "NO",               "TK_NO",           FKEY|WINDOWFUNC        },
  { "NOT",              "TK_NOT",          ALWAYS                 },
  { "NOTHING",          "TK_NOTHING",      UPSERT                 },
  { "NOTNULL",          "TK_NOTNULL",      ALWAYS                 },
  { "NULL",             "TK_NULL",         ALWAYS                 },
  { "NULLS",            "TK_NULLS",        ALWAYS                 },
  { "OF",               "TK_OF",           ALWAYS                 },
  { "OFFSET",           "TK_OFFSET",       ALWAYS                 },
  { "ON",               "TK_ON",           ALWAYS                 },
  { "OR",               "TK_OR",           ALWAYS                 },
  { "ORDER",            "TK_ORDER",        ALWAYS                 },
  { "OTHERS",           "TK_OTHERS",       WINDOWFUNC             },
  { "OUTER",            "TK_JOIN_KW",      ALWAYS                 },