# [fpc-devel] FormatFloat

Thu Dec 31 00:04:00 CET 2009

```>
> On 30 Dec 2009, at 18:25, darekm at emadar.com wrote:
>
>>>
>>> On 30 Dec 2009, at 17:27, darekm at emadar.com wrote:
>>>
>>>> this program:
>>>> var
>>>> d1,d2 : double;
>>    d1,d2 : extended;
>>>> begin
>>>> d1:=105;
>>>> d2:=1.05e2;
>>>> writeln(d1-d2);
>>>> end;
>>>
>>> result: 6.9388939907E-18
>>
>> sorry,
>> I did not notice, that is different type (extended)
>>
>> version 2.5.1 [2009/11/05] (linux and windows)
>
> Ok, now I can reproduce it. It's caused by the fact that 1.05 cannot be
> represented exactly. 1.05e2 is first parsed as 1.05, and then multplied by
> 100. So you get an maximal error of extended_precision_delta*100. In that
> situation 6.9388939907E-18 is acceptable (extended_precision_delta is
> 1.0842021725e-19). The fact that the result is equal in case of double is
> simply because due to less available precision, the 1.05 value happens to
> be is rounded in a different way and 100*1.05 turns out the same as 105.0
>
> Delphi apparently parses 1.05e2 in a different way (maybe it performs the
> "e2" multiplication on the string representation in order to minimise
> losses due to limited precision).

I look at fpc_val_real_shortstr, which I think is used to convert form str
to real
Its seems ease to change:
after decimal part of number is computed divide  by length of fractional
part should be moved to part of exponent (simply correct of exponent)

Try the following program and you'll see
> that for the second subtraction, Delphi gives the same result as FPC:
>
> var
>  d1,d2,d3 : extended;
> begin
>  d1:=105;
>  d2:=1.05e2;
>  d3:=1.05;
>  d3:=d3*100.0;
>  writeln(d1-d2);
>  writeln(d2-d3);
> end.
>
> Both results are correct in the context of IEEE floating point math.

That is different
1.05e2 is natural number, and 1.05 not
for natural number (till limit) we can expect equal representation

Darek

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