SQLite

    case TK_AGG_COLUMN: {
      AggInfo *pAggInfo = pExpr->pAggInfo;
      struct AggInfo_col *pCol;
      assert( pAggInfo!=0 );
      assert( pExpr->iAgg>=0 && pExpr->iAgg<pAggInfo->nColumn );
      pCol = &pAggInfo->aCol[pExpr->iAgg];
      if( !pAggInfo->directMode ){
        assert( pCol->iMem>0 );
        return pCol->iMem;
      }else if( pAggInfo->useSortingIdx ){
        Table *pTab = pCol->pTab;
        sqlite3VdbeAddOp3(v, OP_Column, pAggInfo->sortingIdxPTab,
                              pCol->iSorterColumn, target);
        if( pCol->iColumn<0 ){
          VdbeComment((v,"%s.rowid",pTab->zName));
        }else if( ALWAYS(pTab!=0) ){

      if( pInfo==0
       || NEVER(pExpr->iAgg<0)
       || NEVER(pExpr->iAgg>=pInfo->nFunc)
      ){
        assert( !ExprHasProperty(pExpr, EP_IntValue) );
        sqlite3ErrorMsg(pParse, "misuse of aggregate: %#T()", pExpr);
      }else{
        assert( pInfo->aFunc[pExpr->iAgg].iMem>0 );
        return pInfo->aFunc[pExpr->iAgg].iMem;
      }
      break;
    }
    case TK_FUNCTION: {
      ExprList *pFarg;       /* List of function arguments */
      int nFarg;             /* Number of function arguments */
      FuncDef *pDef;         /* The function definition object */

    case TK_IF_NULL_ROW: {
      int addrINR;
      u8 okConstFactor = pParse->okConstFactor;
      AggInfo *pAggInfo = pExpr->pAggInfo;
      if( pAggInfo ){
        assert( pExpr->iAgg>=0 && pExpr->iAgg<pAggInfo->nColumn );
        if( !pAggInfo->directMode ){
          assert( pAggInfo->aCol[pExpr->iAgg].iMem>0 );
          inReg = pAggInfo->aCol[pExpr->iAgg].iMem;
          break;
        }
        if( pExpr->pAggInfo->useSortingIdx ){
          sqlite3VdbeAddOp3(v, OP_Column, pAggInfo->sortingIdxPTab,
                            pAggInfo->aCol[pExpr->iAgg].iSorterColumn,
                            target);
          inReg = target;

}

/*
** Assign register numbers to all pAggInfo->aCol[] and pAggInfo->aFunc[]
** entries.
*/
static void assignAggregateRegisters(Parse *pParse, AggInfo *pAggInfo){
  int i, m;
  assert( pAggInfo!=0 );

  m = pParse->nMem;
  for(i=0; i<pAggInfo->nColumn; i++) pAggInfo->aCol[i].iMem = ++m;
  for(i=0; i<pAggInfo->nFunc; i++) pAggInfo->aFunc[i].iMem = ++m;
  pParse->nMem = m;
}

/*
** Reset the aggregate accumulator.
**
** The aggregate accumulator is a set of memory cells that hold
** intermediate results while calculating an aggregate.  This
** routine generates code that stores NULLs in all of those memory
** cells.
*/
static void resetAccumulator(Parse *pParse, AggInfo *pAggInfo){
  Vdbe *v = pParse->pVdbe;
  int i;
  int iFirstReg;
  struct AggInfo_func *pFunc;
  int nReg = pAggInfo->nFunc + pAggInfo->nColumn;
  assert( pParse->db->pParse==pParse );
  assert( pParse->db->mallocFailed==0 || pParse->nErr!=0 );
  if( nReg==0 ) return;

  if( pParse->nErr ) return;
  if( pAggInfo->nColumn==0 ){
    iFirstReg = pAggInfo->aFunc[0].iMem;
  }else{
    iFirstReg = pAggInfo->aCol[0].iMem;
  }
#ifdef SQLITE_DEBUG
  /* Verify that all AggInfo register numbers have been assigned and that
  ** they are all sequential. */
  assert( iFirstReg>0 );
  for(i=0; i<pAggInfo->nColumn; i++){
    assert( pAggInfo->aCol[i].iMem>=iFirstReg );
    assert( i==0 || pAggInfo->aCol[i].iMem==pAggInfo->aCol[i-1].iMem+1 );
  }
  for(i=0; i<pAggInfo->nFunc; i++){
    assert( pAggInfo->aFunc[i].iMem>=iFirstReg );
    assert( i>0 || pAggInfo->nColumn==0
      || pAggInfo->aFunc[i].iMem==pAggInfo->aCol[pAggInfo->nColumn-1].iMem+1 );
    assert( i==0 || pAggInfo->aFunc[i].iMem==pAggInfo->aFunc[i-1].iMem+1 );
  }
#endif
  sqlite3VdbeAddOp3(v, OP_Null, 0, iFirstReg, iFirstReg+nReg-1);

  for(pFunc=pAggInfo->aFunc, i=0; i<pAggInfo->nFunc; i++, pFunc++){
    if( pFunc->iDistinct>=0 ){
      Expr *pE = pFunc->pFExpr;
      assert( ExprUseXList(pE) );
      if( pE->x.pList==0 || pE->x.pList->nExpr!=1 ){
        sqlite3ErrorMsg(pParse, "DISTINCT aggregates must have exactly one "
           "argument");

  Vdbe *v = pParse->pVdbe;
  int i;
  struct AggInfo_func *pF;
  for(i=0, pF=pAggInfo->aFunc; i<pAggInfo->nFunc; i++, pF++){
    ExprList *pList;
    assert( ExprUseXList(pF->pFExpr) );
    pList = pF->pFExpr->x.pList;
    sqlite3VdbeAddOp2(v, OP_AggFinal, pF->iMem, pList ? pList->nExpr : 0);

    sqlite3VdbeAppendP4(v, pF->pFunc, P4_FUNCDEF);
  }
}


/*
** Update the accumulator memory cells for an aggregate based on

      }
      if( !pColl ){
        pColl = pParse->db->pDfltColl;
      }
      if( regHit==0 && pAggInfo->nAccumulator ) regHit = ++pParse->nMem;
      sqlite3VdbeAddOp4(v, OP_CollSeq, regHit, 0, 0, (char *)pColl, P4_COLLSEQ);
    }
    sqlite3VdbeAddOp3(v, OP_AggStep, 0, regAgg, pF->iMem);
    sqlite3VdbeAppendP4(v, pF->pFunc, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, (u8)nArg);
    sqlite3ReleaseTempRange(pParse, regAgg, nArg);
    if( addrNext ){
      sqlite3VdbeResolveLabel(v, addrNext);
    }
  }
  if( regHit==0 && pAggInfo->nAccumulator ){
    regHit = regAcc;
  }
  if( regHit ){
    addrHitTest = sqlite3VdbeAddOp1(v, OP_If, regHit); VdbeCoverage(v);
  }
  for(i=0, pC=pAggInfo->aCol; i<pAggInfo->nAccumulator; i++, pC++){
    sqlite3ExprCode(pParse, pC->pCExpr, pC->iMem);
  }

  pAggInfo->directMode = 0;
  if( addrHitTest ){
    sqlite3VdbeJumpHereOrPopInst(v, addrHitTest);
  }
}

  int ii;
  for(ii=0; ii<pAggInfo->nColumn; ii++){
    struct AggInfo_col *pCol = &pAggInfo->aCol[ii];
    sqlite3DebugPrintf(
       "agg-column[%d] pTab=%s iTable=%d iColumn=%d iMem=%d"
       " iSorterColumn=%d\n",
       ii, pCol->pTab ? pCol->pTab->zName : "NULL", 
       pCol->iTable, pCol->iColumn, pCol->iMem,
       pCol->iSorterColumn);
    sqlite3TreeViewExpr(0, pAggInfo->aCol[ii].pCExpr, 0);
  }
  for(ii=0; ii<pAggInfo->nFunc; ii++){
    sqlite3DebugPrintf("agg-func[%d]: iMem=%d\n",
        ii, pAggInfo->aFunc[ii].iMem);
    sqlite3TreeViewExpr(0, pAggInfo->aFunc[ii].pFExpr, 0);
  }
}
#endif /* TREETRACE_ENABLED */

/*
** Generate code for the SELECT statement given in the p argument.  

        /* Open a read-only cursor, execute the OP_Count, close the cursor. */
        sqlite3VdbeAddOp4Int(v, OP_OpenRead, iCsr, (int)iRoot, iDb, 1);
        if( pKeyInfo ){
          sqlite3VdbeChangeP4(v, -1, (char *)pKeyInfo, P4_KEYINFO);
        }
        assignAggregateRegisters(pParse, pAggInfo);
        assert( pAggInfo->aFunc[0].iMem>=0 );
        sqlite3VdbeAddOp2(v, OP_Count, iCsr, pAggInfo->aFunc[0].iMem);
        sqlite3VdbeAddOp1(v, OP_Close, iCsr);
        explainSimpleCount(pParse, pTab, pBest);
      }else{
        int regAcc = 0;           /* "populate accumulators" flag */
        ExprList *pDistinct = 0;
        u16 distFlag = 0;
        int eDist;

** fields do not need to be freed when deallocating the AggInfo structure.
*/
struct AggInfo {
  u8 directMode;          /* Direct rendering mode means take data directly
                          ** from source tables rather than from accumulators */
  u8 useSortingIdx;       /* In direct mode, reference the sorting index rather
                          ** than the source table */

  int sortingIdx;         /* Cursor number of the sorting index */
  int sortingIdxPTab;     /* Cursor number of pseudo-table */
  int nSortingColumn;     /* Number of columns in the sorting index */

  ExprList *pGroupBy;     /* The group by clause */
  struct AggInfo_col {    /* For each column used in source tables */
    Table *pTab;             /* Source table */
    Expr *pCExpr;            /* The original expression */
    int iTable;              /* Cursor number of the source table */
    int iMem;                /* Memory location that acts as accumulator */
    i16 iColumn;             /* Column number within the source table */
    i16 iSorterColumn;       /* Column number in the sorting index */
  } *aCol;
  int nColumn;            /* Number of used entries in aCol[] */
  int nAccumulator;       /* Number of columns that show through to the output.
                          ** Additional columns are used only as parameters to
                          ** aggregate functions */
  struct AggInfo_func {   /* For each aggregate function */
    Expr *pFExpr;            /* Expression encoding the function */
    FuncDef *pFunc;          /* The aggregate function implementation */
    int iMem;                /* Memory location that acts as accumulator */
    int iDistinct;           /* Ephemeral table used to enforce DISTINCT */
    int iDistAddr;           /* Address of OP_OpenEphemeral */
  } *aFunc;
  int nFunc;              /* Number of entries in aFunc[] */
  u32 selId;              /* Select to which this AggInfo belongs */
};







/*
** The datatype ynVar is a signed integer, either 16-bit or 32-bit.
** Usually it is 16-bits.  But if SQLITE_MAX_VARIABLE_NUMBER is greater
** than 32767 we have to make it 32-bit.  16-bit is preferred because
** it uses less memory in the Expr object, which is a big memory user
** in systems with lots of prepared statements.  And few applications
** need more than about 10 or 20 variables.  But some extreme users want