SQLite

    "frame ending offset must be a non-negative integer"
  };
  Vdbe *v = sqlite3GetVdbe(pParse);
  int regZero = sqlite3GetTempReg(pParse);
  sqlite3VdbeAddOp2(v, OP_Integer, 0, regZero);
  sqlite3VdbeAddOp2(v, OP_MustBeInt, reg, sqlite3VdbeCurrentAddr(v)+2);
  sqlite3VdbeAddOp3(v, OP_Ge, regZero, sqlite3VdbeCurrentAddr(v)+2, reg);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_Halt, SQLITE_ERROR, OE_Abort);
  sqlite3VdbeAppendP4(v, (void*)azErr[bEnd], P4_STATIC);
  sqlite3ReleaseTempReg(pParse, regZero);
}

/*
** Return the number of arguments passed to the window-function associated

      if( bInverse==0 ){
        sqlite3VdbeAddOp2(v, OP_AddImm, pWin->regApp+1, 1);
        sqlite3VdbeAddOp2(v, OP_SCopy, regArg, pWin->regApp);
        sqlite3VdbeAddOp3(v, OP_MakeRecord, pWin->regApp, 2, pWin->regApp+2);
        sqlite3VdbeAddOp2(v, OP_IdxInsert, pWin->csrApp, pWin->regApp+2);
      }else{
        sqlite3VdbeAddOp4Int(v, OP_SeekGE, pWin->csrApp, 0, regArg, 1);
        VdbeCoverage(v);
        sqlite3VdbeAddOp1(v, OP_Delete, pWin->csrApp);
        sqlite3VdbeJumpHere(v, sqlite3VdbeCurrentAddr(v)-2);
      }
    }else if( pWin->regApp ){
      assert( pWin->pFunc->xSFunc==nth_valueStepFunc 
           || pWin->pFunc->xSFunc==first_valueStepFunc 
      );

        if( csr>0 ){
          regTmp = sqlite3GetTempReg(pParse);
          sqlite3VdbeAddOp3(v, OP_Column, csr, pWin->iArgCol+nArg,regTmp);
        }else{
          regTmp = regArg + nArg;
        }
        addrIf = sqlite3VdbeAddOp3(v, OP_IfNot, regTmp, 0, 1);
        VdbeCoverage(v);
        if( csr>0 ){
          sqlite3ReleaseTempReg(pParse, regTmp);
        }
      }
      if( pWin->pFunc->funcFlags & SQLITE_FUNC_NEEDCOLL ){
        CollSeq *pColl;
        pColl = sqlite3ExprNNCollSeq(pParse, pWin->pOwner->x.pList->a[0].pExpr);

  for(pWin=pMWin; pWin; pWin=pWin->pNextWin){
    if( (pWin->pFunc->funcFlags & SQLITE_FUNC_MINMAX) 
     && pWin->eStart!=TK_UNBOUNDED 
    ){
      sqlite3VdbeAddOp2(v, OP_Null, 0, pWin->regResult);
      sqlite3VdbeAddOp1(v, OP_Last, pWin->csrApp);
      VdbeCoverage(v);
      sqlite3VdbeAddOp3(v, OP_Column, pWin->csrApp, 0, pWin->regResult);
      sqlite3VdbeJumpHere(v, sqlite3VdbeCurrentAddr(v)-2);
      if( bFinal ){
        sqlite3VdbeAddOp1(v, OP_ResetSorter, pWin->csrApp);
      }
    }else if( pWin->regApp ){
    }else{

    int nPart = pPart->nExpr;
    int regNewPart = reg + pMWin->nBufferCol;
    KeyInfo *pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pPart, 0, 0);

    addr = sqlite3VdbeAddOp3(v, OP_Compare, regNewPart, pMWin->regPart,nPart);
    sqlite3VdbeAppendP4(v, (void*)pKeyInfo, P4_KEYINFO);
    sqlite3VdbeAddOp3(v, OP_Jump, addr+2, addr+4, addr+2);
    VdbeCoverage(v);
    sqlite3VdbeAddOp3(v, OP_Copy, regNewPart, pMWin->regPart, nPart-1);
    sqlite3VdbeAddOp2(v, OP_Gosub, regFlushPart, lblFlushPart);
  }

  /* Buffer the current row in the ephemeral table. */
  sqlite3VdbeAddOp2(v, OP_NewRowid, pMWin->iEphCsr, regRowid);
  sqlite3VdbeAddOp3(v, OP_Insert, pMWin->iEphCsr, regRecord, regRowid);

      if( pFunc->xSFunc==nth_valueStepFunc ){
        sqlite3VdbeAddOp3(v, OP_Column, pMWin->iEphCsr, pWin->iArgCol+1,tmpReg);
      }else{
        sqlite3VdbeAddOp2(v, OP_Integer, 1, tmpReg);
      }
      sqlite3VdbeAddOp3(v, OP_Add, tmpReg, pWin->regApp, tmpReg);
      sqlite3VdbeAddOp3(v, OP_Gt, pWin->regApp+1, lbl, tmpReg);
      VdbeCoverage(v);
      sqlite3VdbeAddOp3(v, OP_SeekRowid, csr, lbl, tmpReg);
      VdbeCoverage(v);
      sqlite3VdbeAddOp3(v, OP_Column, csr, pWin->iArgCol, pWin->regResult);
      sqlite3VdbeResolveLabel(v, lbl);
      sqlite3ReleaseTempReg(pParse, tmpReg);
    }
    else if( pFunc->xSFunc==leadStepFunc || pFunc->xSFunc==lagStepFunc ){
      int nArg = pWin->pOwner->x.pList->nExpr;
      int iEph = pMWin->iEphCsr;

        int tmpReg2 = sqlite3GetTempReg(pParse);
        sqlite3VdbeAddOp3(v, OP_Column, iEph, pWin->iArgCol+1, tmpReg2);
        sqlite3VdbeAddOp3(v, op, tmpReg2, tmpReg, tmpReg);
        sqlite3ReleaseTempReg(pParse, tmpReg2);
      }

      sqlite3VdbeAddOp3(v, OP_SeekRowid, csr, lbl, tmpReg);
      VdbeCoverage(v);
      sqlite3VdbeAddOp3(v, OP_Column, csr, pWin->iArgCol, pWin->regResult);
      sqlite3VdbeResolveLabel(v, lbl);
      sqlite3ReleaseTempReg(pParse, tmpReg);
    }
  }
  sqlite3VdbeAddOp2(v, OP_Gosub, regGosub, addrGosub);
}

  int regInvArg,                  /* Array of registers for xInverse args */
  int regInvSize                  /* Register containing size of partition */
){
  int addr;
  Vdbe *v = sqlite3GetVdbe(pParse);
  windowAggFinal(pParse, pMWin, 0);
  addr = sqlite3VdbeAddOp3(v, OP_IfPos, regCtr, sqlite3VdbeCurrentAddr(v)+2 ,1);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_Goto, 0, 0);
  windowReturnOneRow(pParse, pMWin, regGosub, addrGosub);
  if( regInvArg ){
    windowAggStep(pParse, pMWin, pMWin->iEphCsr, 1, regInvArg, regInvSize);
  }
  sqlite3VdbeAddOp2(v, OP_Next, pMWin->iEphCsr, addr);
  VdbeCoverage(v);
  sqlite3VdbeJumpHere(v, addr+1);   /* The OP_Goto */
}

/*
** Generate code to set the accumulator register for each window function
** in the linked list passed as the second argument to NULL. And perform
** any equivalent initialization required by any built-in window functions

  windowPartitionCache(pParse, p, pWInfo, regFlushPart, lblFlushPart, &regSize);

  addrGoto = sqlite3VdbeAddOp0(v, OP_Goto);

  /* Start of "flush_partition" */
  sqlite3VdbeResolveLabel(v, lblFlushPart);
  sqlite3VdbeAddOp2(v, OP_Once, 0, sqlite3VdbeCurrentAddr(v)+3);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_OpenDup, csrStart, pMWin->iEphCsr);
  sqlite3VdbeAddOp2(v, OP_OpenDup, csrEnd, pMWin->iEphCsr);

  /* If either regStart or regEnd are not non-negative integers, throw 
  ** an exception.  */
  if( pMWin->pStart ){
    sqlite3ExprCode(pParse, pMWin->pStart, regStart);

  **     regStart = regSize;
  **   }
  **   regEnd = regEnd - regStart;
  */
  if( pMWin->pEnd && pMWin->pStart && pMWin->eStart==TK_FOLLOWING ){
    assert( pMWin->eEnd==TK_FOLLOWING );
    sqlite3VdbeAddOp3(v, OP_Ge, regStart, sqlite3VdbeCurrentAddr(v)+2, regEnd);
    VdbeCoverage(v);
    sqlite3VdbeAddOp2(v, OP_Copy, regSize, regStart);
    sqlite3VdbeAddOp3(v, OP_Subtract, regStart, regEnd, regEnd);
  }

  if( pMWin->pEnd && pMWin->pStart && pMWin->eEnd==TK_PRECEDING ){
    assert( pMWin->eStart==TK_PRECEDING );
    sqlite3VdbeAddOp3(v, OP_Le, regStart, sqlite3VdbeCurrentAddr(v)+3, regEnd);
    VdbeCoverage(v);
    sqlite3VdbeAddOp2(v, OP_Copy, regSize, regStart);
    sqlite3VdbeAddOp2(v, OP_Copy, regSize, regEnd);
  }

  /* Initialize the accumulator register for each window function to NULL */
  regArg = windowInitAccum(pParse, pMWin);

  sqlite3VdbeAddOp2(v, OP_Rewind, pMWin->iEphCsr, lblFlushDone);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_Rewind, csrStart, lblFlushDone);
  VdbeCoverageNeverTaken(v);
  sqlite3VdbeChangeP5(v, 1);
  sqlite3VdbeAddOp2(v, OP_Rewind, csrEnd, lblFlushDone);
  VdbeCoverageNeverTaken(v);
  sqlite3VdbeChangeP5(v, 1);

  /* Invoke AggStep function for each window function using the row that
  ** csrEnd currently points to. Or, if csrEnd is already at EOF,
  ** do nothing.  */
  addrTop = sqlite3VdbeCurrentAddr(v);
  if( pMWin->eEnd==TK_PRECEDING ){
    addrIfPos1 = sqlite3VdbeAddOp3(v, OP_IfPos, regEnd, 0 , 1);
    VdbeCoverage(v);
  }
  sqlite3VdbeAddOp2(v, OP_Next, csrEnd, sqlite3VdbeCurrentAddr(v)+2);
  VdbeCoverage(v);
  addr = sqlite3VdbeAddOp0(v, OP_Goto);
  windowAggStep(pParse, pMWin, csrEnd, 0, regArg, regSize);
  if( pMWin->eEnd==TK_UNBOUNDED ){
    sqlite3VdbeAddOp2(v, OP_Goto, 0, addrTop);
    sqlite3VdbeJumpHere(v, addr);
    addrTop = sqlite3VdbeCurrentAddr(v);
  }else{
    sqlite3VdbeJumpHere(v, addr);
    if( pMWin->eEnd==TK_PRECEDING ){
      sqlite3VdbeJumpHere(v, addrIfPos1);
    }
  }

  if( pMWin->eEnd==TK_FOLLOWING ){
    addrIfPos1 = sqlite3VdbeAddOp3(v, OP_IfPos, regEnd, 0 , 1);
    VdbeCoverage(v);
  }
  if( pMWin->eStart==TK_FOLLOWING ){
    addrIfPos2 = sqlite3VdbeAddOp3(v, OP_IfPos, regStart, 0 , 1);
    VdbeCoverage(v);
  }
  windowAggFinal(pParse, pMWin, 0);
  windowReturnOneRow(pParse, pMWin, regGosub, addrGosub);
  sqlite3VdbeAddOp2(v, OP_Next, pMWin->iEphCsr, sqlite3VdbeCurrentAddr(v)+2);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_Goto, 0, lblFlushDone);
  if( pMWin->eStart==TK_FOLLOWING ){
    sqlite3VdbeJumpHere(v, addrIfPos2);
  }

  if( pMWin->eStart==TK_CURRENT 
   || pMWin->eStart==TK_PRECEDING 
   || pMWin->eStart==TK_FOLLOWING 
  ){
    int addrJumpHere = 0;
    if( pMWin->eStart==TK_PRECEDING ){
      addrJumpHere = sqlite3VdbeAddOp3(v, OP_IfPos, regStart, 0 , 1);
      VdbeCoverage(v);
    }
    sqlite3VdbeAddOp2(v, OP_Next, csrStart, sqlite3VdbeCurrentAddr(v)+1);
    VdbeCoverage(v);
    windowAggStep(pParse, pMWin, csrStart, 1, regArg, regSize);
    if( addrJumpHere ){
      sqlite3VdbeJumpHere(v, addrJumpHere);
    }
  }
  if( pMWin->eEnd==TK_FOLLOWING ){
    sqlite3VdbeJumpHere(v, addrIfPos1);

  windowPartitionCache(pParse, p, pWInfo, regFlushPart, lblFlushPart, &regSize);
  addrGoto = sqlite3VdbeAddOp0(v, OP_Goto);

  /* Start of "flush_partition" */
  sqlite3VdbeResolveLabel(v, lblFlushPart);
  sqlite3VdbeAddOp2(v, OP_Once, 0, sqlite3VdbeCurrentAddr(v)+2);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_OpenDup, csrLead, pMWin->iEphCsr);

  /* Initialize the accumulator register for each window function to NULL */
  regArg = windowInitAccum(pParse, pMWin);

  sqlite3VdbeAddOp2(v, OP_Integer, 0, regCtr);
  sqlite3VdbeAddOp2(v, OP_Rewind, csrLead, lblEmpty);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_Rewind, pMWin->iEphCsr, lblEmpty);
  VdbeCoverageNeverTaken(v);

  if( bReverse ){
    int addr = sqlite3VdbeCurrentAddr(v);
    windowAggStep(pParse, pMWin, csrLead, 0, regArg, regSize);
    sqlite3VdbeAddOp2(v, OP_Next, csrLead, addr);
    VdbeCoverage(v);
    sqlite3VdbeAddOp2(v, OP_Rewind, csrLead, lblEmpty);
    VdbeCoverageNeverTaken(v);
  }
  addrNext = sqlite3VdbeCurrentAddr(v);

  if( pOrderBy && (pMWin->eEnd==TK_CURRENT || pMWin->eStart==TK_CURRENT) ){
    int bCurrent = (pMWin->eStart==TK_CURRENT);
    int addrJump = 0;             /* Address of OP_Jump below */
    if( pMWin->eType==TK_RANGE ){
      int iOff = pMWin->nBufferCol + (pPart ? pPart->nExpr : 0);
      int regPeer = pMWin->regPart + (pPart ? pPart->nExpr : 0);
      KeyInfo *pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pOrderBy, 0, 0);
      for(k=0; k<nPeer; k++){
        sqlite3VdbeAddOp3(v, OP_Column, csrLead, iOff+k, regNewPeer+k);
      }
      addr = sqlite3VdbeAddOp3(v, OP_Compare, regNewPeer, regPeer, nPeer);
      sqlite3VdbeAppendP4(v, (void*)pKeyInfo, P4_KEYINFO);
      addrJump = sqlite3VdbeAddOp3(v, OP_Jump, addr+2, 0, addr+2);
      VdbeCoverage(v);
      sqlite3VdbeAddOp3(v, OP_Copy, regNewPeer, regPeer, nPeer-1);
    }

    windowReturnRows(pParse, pMWin, regCtr, regGosub, addrGosub, 
        (bCurrent ? regArg : 0), (bCurrent ? regSize : 0)
    );
    if( addrJump ) sqlite3VdbeJumpHere(v, addrJump);
  }

  if( bReverse==0 ){
    windowAggStep(pParse, pMWin, csrLead, 0, regArg, regSize);
  }
  sqlite3VdbeAddOp2(v, OP_AddImm, regCtr, 1);
  sqlite3VdbeAddOp2(v, OP_Next, csrLead, addrNext);
  VdbeCoverage(v);

  windowReturnRows(pParse, pMWin, regCtr, regGosub, addrGosub, 0, 0);

  sqlite3VdbeResolveLabel(v, lblEmpty);
  sqlite3VdbeAddOp1(v, OP_ResetSorter, pMWin->iEphCsr);
  sqlite3VdbeAddOp1(v, OP_Return, regFlushPart);

    if( pPart ){
      int regNewPart = reg + pMWin->nBufferCol;
      KeyInfo *pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pPart, 0, 0);
      addr = sqlite3VdbeAddOp3(v, OP_Compare, regNewPart, pMWin->regPart,nPart);
      sqlite3VdbeAppendP4(v, (void*)pKeyInfo, P4_KEYINFO);
      addrJump = sqlite3VdbeAddOp3(v, OP_Jump, addr+2, 0, addr+2);
      VdbeCoverage(v);
      windowAggFinal(pParse, pMWin, 1);
      if( pOrderBy ){
        addrGoto = sqlite3VdbeAddOp0(v, OP_Goto);
      }
    }

    if( pOrderBy ){
      int regNewPeer = reg + pMWin->nBufferCol + nPart;
      int regPeer = pMWin->regPart + nPart;

      if( addrJump ) sqlite3VdbeJumpHere(v, addrJump);
      if( pMWin->eType==TK_RANGE ){
        KeyInfo *pKeyInfo = sqlite3KeyInfoFromExprList(pParse, pOrderBy, 0, 0);
        addr = sqlite3VdbeAddOp3(v, OP_Compare, regNewPeer, regPeer, nPeer);
        sqlite3VdbeAppendP4(v, (void*)pKeyInfo, P4_KEYINFO);
        addrJump = sqlite3VdbeAddOp3(v, OP_Jump, addr+2, 0, addr+2);
        VdbeCoverage(v);
      }else{
        addrJump = 0;
      }
      windowAggFinal(pParse, pMWin, pMWin->eStart==TK_CURRENT);
      if( addrGoto ) sqlite3VdbeJumpHere(v, addrGoto);
    }

    sqlite3VdbeAddOp2(v, OP_Rewind, pMWin->iEphCsr,sqlite3VdbeCurrentAddr(v)+3);
    VdbeCoverage(v);
    sqlite3VdbeAddOp2(v, OP_Gosub, regGosub, addrGosub);
    sqlite3VdbeAddOp2(v, OP_Next, pMWin->iEphCsr, sqlite3VdbeCurrentAddr(v)-1);
    VdbeCoverage(v);

    sqlite3VdbeAddOp1(v, OP_ResetSorter, pMWin->iEphCsr);
    sqlite3VdbeAddOp3(
        v, OP_Copy, reg+pMWin->nBufferCol, pMWin->regPart, nPart+nPeer-1
    );

    if( addrJump ) sqlite3VdbeJumpHere(v, addrJump);

  sqlite3VdbeAddOp3(v, OP_Insert, pMWin->iEphCsr, regRecord, regRowid);

  /* End the database scan loop. */
  sqlite3WhereEnd(pWInfo);

  windowAggFinal(pParse, pMWin, 1);
  sqlite3VdbeAddOp2(v, OP_Rewind, pMWin->iEphCsr,sqlite3VdbeCurrentAddr(v)+3);
  VdbeCoverage(v);
  sqlite3VdbeAddOp2(v, OP_Gosub, regGosub, addrGosub);
  sqlite3VdbeAddOp2(v, OP_Next, pMWin->iEphCsr, sqlite3VdbeCurrentAddr(v)-1);
  VdbeCoverage(v);
}

/*
** Allocate and return a duplicate of the Window object indicated by the
** third argument. Set the Window.pOwner field of the new object to
** pOwner.
*/