#### Delphi XE2 Rounding with DecimalRounding_JH1 

```Because of a documented rounding issue in Delphi XE2, we are using a special rounding unit available on the Embarcadero site named DecimalRounding_JH1 (Thank you John Herbster!) to achieve true bankers rounding.

Using this unit's DecimalRound function with numbers containing a large number of decimal place we get a floating point error.

This is the rounding routine from the DecimalRounding_JH1 unit. In our example we call this DecimalRound function with the following parameters (166426800, 12, MaxRelErrDbl, drHalfEven) where maxRelErrDbl = 2.2204460493e-16 * 1.234375 * 2

{code}

Function DecimalRound(Value: extended; NDFD: integer; MaxRelErr: double;
Ctrl: tDecimalRoundingCtrl = drHalfEven): extended;
{ The DecimalRounding function is for doing the best possible job of rounding
floating binary point numbers to the specified (NDFD) number of decimal
fraction digits.  MaxRelErr is the maximum relative error that will allowed
when determining when to apply the rounding rule.  }
var i64, j64: Int64; k: integer; m, ScaledVal, ScaledErr: extended;
begin

If IsNaN(Value) or (Ctrl = drNone)
then begin Result := Value; EXIT end;

Assert(MaxRelErr > 0,
'MaxRelErr param in call to DecimalRound() must be greater than zero.');

{ Compute 10^NDFD and scale the Value and MaxError: }
m := 1; For k := 1 to abs(NDFD) do m := m*10;
If NDFD >= 0
then begin
ScaledVal := Value * m;
ScaledErr := abs(MaxRelErr*Value) * m;
end
else begin
ScaledVal := Value / m;
ScaledErr := abs(MaxRelErr*Value) / m;
end;

{ Do the diferent basic types separately: }
Case Ctrl of
drHalfEven: begin
**i64 := round((ScaledVal - ScaledErr));**
{code}

The last line is where we get a floating point error.

Any thoughts on why this error is occurring?

Edited by: Jeff Cope on Jul 8, 2013 5:23 AM
```
 0
Jeff
7/8/2013 12:24:07 PM

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