}
  }
  return nChng;
}
#endif /* !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) */

/*
** Based on the contents of the AggInfo structure indicated by the first
** argument, this function checks if the following are true:
**
**    * the query contains just a single aggregate function,
**    * the aggregate function is either min() or max(), and
**    * the argument to the aggregate function is a column value.
**
** If all of the above are true, then WHERE_ORDERBY_MIN or WHERE_ORDERBY_MAX
** is returned as appropriate. Also, *ppMinMax is set to point to the 
** list of arguments passed to the aggregate before returning.
**
** Or, if the conditions above are not met, *ppMinMax is set to 0 and
** WHERE_ORDERBY_NORMAL is returned.
*/
static u8 minMaxQuery(AggInfo *pAggInfo, ExprList **ppMinMax){
  int eRet = WHERE_ORDERBY_NORMAL;          /* Return value */

  *ppMinMax = 0;
  if( pAggInfo->nFunc==1 ){
    Expr *pExpr = pAggInfo->aFunc[0].pExpr; /* Aggregate function */
    ExprList *pEList = pExpr->x.pList;      /* Arguments to agg function */

    assert( pExpr->op==TK_AGG_FUNCTION );
    if( pEList && pEList->nExpr==1 && pEList->a[0].pExpr->op==TK_AGG_COLUMN ){
      const char *zFunc = pExpr->u.zToken;
      if( sqlite3StrICmp(zFunc, "min")==0 ){
        eRet = WHERE_ORDERBY_MIN;
        *ppMinMax = pEList;
      }else if( sqlite3StrICmp(zFunc, "max")==0 ){
        eRet = WHERE_ORDERBY_MAX;
        *ppMinMax = pEList;
      }
    }
  }

  assert( *ppMinMax==0 || (*ppMinMax)->nExpr==1 );


  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:
................................................................................
  Expr *pHaving;         /* The HAVING clause.  May be NULL */
  int rc = 1;            /* Value to return from this function */
  DistinctCtx sDistinct; /* Info on how to code the DISTINCT keyword */
  SortCtx sSort;         /* Info on how to code the ORDER BY clause */
  AggInfo sAggInfo;      /* Information used by aggregate queries */
  int iEnd;              /* Address of the end of the query */
  sqlite3 *db;           /* The database connection */



#ifndef SQLITE_OMIT_EXPLAIN
  int iRestoreSelectId = pParse->iSelectId;
  pParse->iSelectId = pParse->iNextSelectId++;
#endif

  db = pParse->db;
................................................................................
        assert( pWhere==p->pWhere );
        havingToWhere(pParse, pGroupBy, pHaving, &p->pWhere);
        pWhere = p->pWhere;
      }
      sqlite3ExprAnalyzeAggregates(&sNC, pHaving);
    }
    sAggInfo.nAccumulator = sAggInfo.nColumn;





    for(i=0; i<sAggInfo.nFunc; i++){
      assert( !ExprHasProperty(sAggInfo.aFunc[i].pExpr, EP_xIsSelect) );
      sNC.ncFlags |= NC_InAggFunc;
      sqlite3ExprAnalyzeAggList(&sNC, sAggInfo.aFunc[i].pExpr->x.pList);
      sNC.ncFlags &= ~NC_InAggFunc;
    }
    sAggInfo.mxReg = pParse->nMem;
................................................................................
      */
      sqlite3VdbeResolveLabel(v, addrReset);
      resetAccumulator(pParse, &sAggInfo);
      sqlite3VdbeAddOp1(v, OP_Return, regReset);
     
    } /* endif pGroupBy.  Begin aggregate queries without GROUP BY: */
    else {
      ExprList *pDel = 0;
#ifndef SQLITE_OMIT_BTREECOUNT
      Table *pTab;
      if( (pTab = isSimpleCount(p, &sAggInfo))!=0 ){
        /* If isSimpleCount() returns a pointer to a Table structure, then
        ** the SQL statement is of the form:
        **
        **   SELECT count(*) FROM <tbl>
................................................................................
        }
        sqlite3VdbeAddOp2(v, OP_Count, iCsr, sAggInfo.aFunc[0].iMem);
        sqlite3VdbeAddOp1(v, OP_Close, iCsr);
        explainSimpleCount(pParse, pTab, pBest);
      }else
#endif /* SQLITE_OMIT_BTREECOUNT */
      {
        /* Check if the query is of one of the following forms:
        **
        **   SELECT min(x) FROM ...
        **   SELECT max(x) FROM ...
        **
        ** If it is, then ask the code in where.c to attempt to sort results
        ** as if there was an "ORDER BY x" or "ORDER BY x DESC" clause. 
        ** If where.c is able to produce results sorted in this order, then
        ** add vdbe code to break out of the processing loop after the 
        ** first iteration (since the first iteration of the loop is 
        ** guaranteed to operate on the row with the minimum or maximum 
        ** value of x, the only row required).
        **
        ** A special flag must be passed to sqlite3WhereBegin() to slightly
        ** modify behavior as follows:
        **
        **   + If the query is a "SELECT min(x)", then the loop coded by
        **     where.c should not iterate over any values with a NULL value
        **     for x.
        **
        **   + The optimizer code in where.c (the thing that decides which
        **     index or indices to use) should place a different priority on 
        **     satisfying the 'ORDER BY' clause than it does in other cases.
        **     Refer to code and comments in where.c for details.
        */
        ExprList *pMinMax = 0;
        u8 flag = WHERE_ORDERBY_NORMAL;
        
        assert( p->pGroupBy==0 );
        assert( flag==0 );
        if( p->pHaving==0 ){
          flag = minMaxQuery(&sAggInfo, &pMinMax);
        }
        assert( flag==0 || (pMinMax!=0 && pMinMax->nExpr==1) );

        if( flag ){
          pMinMax = sqlite3ExprListDup(db, pMinMax, 0);
          pDel = pMinMax;
          assert( db->mallocFailed || pMinMax!=0 );
          if( !db->mallocFailed ){
            pMinMax->a[0].sortOrder = flag!=WHERE_ORDERBY_MIN ?1:0;
            pMinMax->a[0].pExpr->op = TK_COLUMN;
          }
        }
  
        /* This case runs if the aggregate has no GROUP BY clause.  The
        ** processing is much simpler since there is only a single row
        ** of output.
        */

        resetAccumulator(pParse, &sAggInfo);









        pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pMinMax, 0,flag,0);

        if( pWInfo==0 ){
          sqlite3ExprListDelete(db, pDel);
          goto select_end;
        }
        updateAccumulator(pParse, &sAggInfo);
        assert( pMinMax==0 || pMinMax->nExpr==1 );
        if( sqlite3WhereIsOrdered(pWInfo)>0 ){
          sqlite3VdbeGoto(v, sqlite3WhereBreakLabel(pWInfo));
          VdbeComment((v, "%s() by index",
                (flag==WHERE_ORDERBY_MIN?"min":"max")));
        }
        sqlite3WhereEnd(pWInfo);
        finalizeAggFunctions(pParse, &sAggInfo);
      }

      sSort.pOrderBy = 0;
      sqlite3ExprIfFalse(pParse, pHaving, addrEnd, SQLITE_JUMPIFNULL);
      selectInnerLoop(pParse, p, -1, 0, 0, 
                      pDest, addrEnd, addrEnd);
      sqlite3ExprListDelete(db, pDel);
    }
    sqlite3VdbeResolveLabel(v, addrEnd);
    
  } /* endif aggregate query */

  if( sDistinct.eTnctType==WHERE_DISTINCT_UNORDERED ){
    explainTempTable(pParse, "DISTINCT");
................................................................................
  rc = (pParse->nErr>0);

  /* Control jumps to here if an error is encountered above, or upon
  ** successful coding of the SELECT.
  */
select_end:
  explainSetInteger(pParse->iSelectId, iRestoreSelectId);

  sqlite3DbFree(db, sAggInfo.aCol);
  sqlite3DbFree(db, sAggInfo.aFunc);
#if SELECTTRACE_ENABLED
  SELECTTRACE(1,pParse,p,("end processing\n"));
  pParse->nSelectIndent--;
#endif
  return rc;
}

    }
  }
  return nChng;
}
#endif /* !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) */

/*
** The pFunc is the only aggregate function in the query.  Check to see
** if the query is a candidate for the min/max optimization. 
**
** If the query is a candidate for the min/max optimization, then set
** *ppMinMax to be an ORDER BY clause to be used for the optimization
** and return either WHERE_ORDERBY_MIN or WHERE_ORDERBY_MAX depending on
** whether pFunc is a min() or max() function.
**
** If the query is not a candidate for the min/max optimization, return
** WHERE_ORDERBY_NORMAL (which must be zero).
**
** This routine must be called after aggregate functions have been
** located but before their arguments have been subjected to aggregate
** analysis.
*/
static u8 minMaxQuery(sqlite3 *db, Expr *pFunc, ExprList **ppMinMax){
  int eRet = WHERE_ORDERBY_NORMAL;      /* Return value */
  ExprList *pEList = pFunc->x.pList;    /* Arguments to agg function */
  const char *zFunc;                    /* Name of aggregate function pFunc */
  ExprList *pOrderBy;
  u8 sortOrder;

  assert( *ppMinMax==0 );
  assert( pFunc->op==TK_AGG_FUNCTION );
  if( pEList==0 || pEList->nExpr!=1 ) return eRet;
  zFunc = pFunc->u.zToken;
  if( sqlite3StrICmp(zFunc, "min")==0 ){
    eRet = WHERE_ORDERBY_MIN;
    sortOrder = SQLITE_SO_ASC;
  }else if( sqlite3StrICmp(zFunc, "max")==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].sortOrder = 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:
................................................................................
  Expr *pHaving;         /* The HAVING clause.  May be NULL */
  int rc = 1;            /* Value to return from this function */
  DistinctCtx sDistinct; /* Info on how to code the DISTINCT keyword */
  SortCtx sSort;         /* Info on how to code the ORDER BY clause */
  AggInfo sAggInfo;      /* Information used by aggregate queries */
  int iEnd;              /* Address of the end of the query */
  sqlite3 *db;           /* The database connection */
  ExprList *pMinMaxOrderBy = 0;  /* Added ORDER BY for min/max queries */
  u8 minMaxFlag;                 /* Flag for min/max queries */

#ifndef SQLITE_OMIT_EXPLAIN
  int iRestoreSelectId = pParse->iSelectId;
  pParse->iSelectId = pParse->iNextSelectId++;
#endif

  db = pParse->db;
................................................................................
        assert( pWhere==p->pWhere );
        havingToWhere(pParse, pGroupBy, pHaving, &p->pWhere);
        pWhere = p->pWhere;
      }
      sqlite3ExprAnalyzeAggregates(&sNC, pHaving);
    }
    sAggInfo.nAccumulator = sAggInfo.nColumn;
    if( p->pGroupBy==0 && p->pHaving==0 && sAggInfo.nFunc==1 ){
      minMaxFlag = minMaxQuery(db, sAggInfo.aFunc[0].pExpr, &pMinMaxOrderBy);
    }else{
      minMaxFlag = WHERE_ORDERBY_NORMAL;
    }
    for(i=0; i<sAggInfo.nFunc; i++){
      assert( !ExprHasProperty(sAggInfo.aFunc[i].pExpr, EP_xIsSelect) );
      sNC.ncFlags |= NC_InAggFunc;
      sqlite3ExprAnalyzeAggList(&sNC, sAggInfo.aFunc[i].pExpr->x.pList);
      sNC.ncFlags &= ~NC_InAggFunc;
    }
    sAggInfo.mxReg = pParse->nMem;
................................................................................
      */
      sqlite3VdbeResolveLabel(v, addrReset);
      resetAccumulator(pParse, &sAggInfo);
      sqlite3VdbeAddOp1(v, OP_Return, regReset);
     
    } /* endif pGroupBy.  Begin aggregate queries without GROUP BY: */
    else {

#ifndef SQLITE_OMIT_BTREECOUNT
      Table *pTab;
      if( (pTab = isSimpleCount(p, &sAggInfo))!=0 ){
        /* If isSimpleCount() returns a pointer to a Table structure, then
        ** the SQL statement is of the form:
        **
        **   SELECT count(*) FROM <tbl>
................................................................................
        }
        sqlite3VdbeAddOp2(v, OP_Count, iCsr, sAggInfo.aFunc[0].iMem);
        sqlite3VdbeAddOp1(v, OP_Close, iCsr);
        explainSimpleCount(pParse, pTab, pBest);
      }else
#endif /* SQLITE_OMIT_BTREECOUNT */
      {













































        /* This case runs if the aggregate has no GROUP BY clause.  The
        ** processing is much simpler since there is only a single row
        ** of output.
        */
        assert( p->pGroupBy==0 );
        resetAccumulator(pParse, &sAggInfo);

        /* If this query is a candidate for the min/max optimization, then
        ** minMaxFlag will have been previously set to either
        ** WHERE_ORDERBY_MIN or WHERE_ORDERBY_MAX and pMinMaxOrderBy will
        ** be an appropriate ORDER BY expression for the optimization.
        */
        assert( minMaxFlag==WHERE_ORDERBY_NORMAL || pMinMaxOrderBy!=0 );
        assert( pMinMaxOrderBy==0 || pMinMaxOrderBy->nExpr==1 );

        pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pMinMaxOrderBy,
                                   0, minMaxFlag, 0);
        if( pWInfo==0 ){

          goto select_end;
        }
        updateAccumulator(pParse, &sAggInfo);

        if( sqlite3WhereIsOrdered(pWInfo)>0 ){
          sqlite3VdbeGoto(v, sqlite3WhereBreakLabel(pWInfo));
          VdbeComment((v, "%s() by index",
                (minMaxFlag==WHERE_ORDERBY_MIN?"min":"max")));
        }
        sqlite3WhereEnd(pWInfo);
        finalizeAggFunctions(pParse, &sAggInfo);
      }

      sSort.pOrderBy = 0;
      sqlite3ExprIfFalse(pParse, pHaving, addrEnd, SQLITE_JUMPIFNULL);
      selectInnerLoop(pParse, p, -1, 0, 0, 
                      pDest, addrEnd, addrEnd);

    }
    sqlite3VdbeResolveLabel(v, addrEnd);
    
  } /* endif aggregate query */

  if( sDistinct.eTnctType==WHERE_DISTINCT_UNORDERED ){
    explainTempTable(pParse, "DISTINCT");
................................................................................
  rc = (pParse->nErr>0);

  /* Control jumps to here if an error is encountered above, or upon
  ** successful coding of the SELECT.
  */
select_end:
  explainSetInteger(pParse->iSelectId, iRestoreSelectId);
  sqlite3ExprListDelete(db, pMinMaxOrderBy);
  sqlite3DbFree(db, sAggInfo.aCol);
  sqlite3DbFree(db, sAggInfo.aFunc);
#if SELECTTRACE_ENABLED
  SELECTTRACE(1,pParse,p,("end processing\n"));
  pParse->nSelectIndent--;
#endif
  return rc;
}

}
do_test minmax2-10.12 {
  execsql {
    SELECT min(x), max(x) FROM t6;
  }
} {{} {}}




































finish_test

}
do_test minmax2-10.12 {
  execsql {
    SELECT min(x), max(x) FROM t6;
  }
} {{} {}}

# 2017-10-26.  Extend the min/max optimization to indexes on expressions
#
do_execsql_test minmax2-11.100 {
  CREATE TABLE t11(a,b,c);
  INSERT INTO t11(a,b,c) VALUES(1,10,5),(2,8,11),(3,1,4),(4,20,1),(5,16,4);
  CREATE INDEX t11bc ON t11(b+c);
  SELECT max(b+c) FROM t11;
} {21}
do_execsql_test minmax2-11.110 {
  SELECT a, max(b+c) FROM t11;
} {4 21}
do_test minmax2-11.111 {
  db eval {SELECT max(b+c) FROM t11}
  db status step
} {0}
do_test minmax2-11.112 {
  db eval {SELECT max(c+b) FROM t11}
  db status step
} {4}
do_execsql_test minmax2-11.120 {
  SELECT a, min(b+c) FROM t11;
} {3 5}
do_test minmax2-11.121 {
  db eval {SELECT min(b+c) FROM t11}
  db status step
} {0}
do_test minmax2-11.122 {
  db eval {SELECT min(c+b) FROM t11}
  db status step
} {4}
do_execsql_test minmax2-11.130 {
  INSERT INTO t11(a,b,c) VALUES(6,NULL,0),(7,0,NULL);
  SELECT a, min(b+c) FROM t11;
} {3 5}

finish_test