[fpc-devel] Rounding inconsistent (critical)

[Vincent Snijders]

Graeme Geldenhuys schreef:
> On 02/10/06, Vincent Snijders <vsnijders at quicknet.nl> wrote:
>> It is not a bug, it is using bankers rounding. See
>> http://lazarus-ccr.sourceforge.net/docs/rtl/system/round.html
>>
>> Vincent
> 
> Exactly, but it is still wrong, except if I really don't know how
> Banker's rounding works and what they mean by Even Number.
> 
> Take these to new tests.
> 
>  AssertEquals('Failing on 10', '0.44', FormatFloat('0.00', 0.445));
>  AssertEquals('Failing on 11', '0.46', FormatFloat('0.00', 0.455));
> 
> Test 10:
>  Fails and said it expected 0.45 instead of my answer 0.44.  Why?
> This is how I came to my answer of 0.44.  I ignore the "0." and only
> look at 445 and I want that to 2 decimal digits. Lets now do what the
> documentation says and go to the closest even number. 44 is even, 45
> is not.  So I would have thought it must round down to 0.44.  It
> doesn't.

by "expected 0.45" you mean "got 0.45", otherwise I don't understand your reasoning.

I don't have an explanation, maybe it is due to rounding errors. 0.445 can not be 
represented exactly using floating point binary numbers.

Can you see if
   AssertEquals('Failing on 10', '0.12', FormatFloat('0.00', 0.125));
and
   AssertEquals('Failing on 10', '0.38', FormatFloat('0.00', 0.375));

work? These number can be represented exactly.

> 
> Test 11:
>  Fails and said it expected 0.45 instead of my answer 0.46.  Again,
> the way I rounded it. Ignore the "0.' and only look at 455.  I want it
> to 2 decimal digits. What is the closest to a even number 45 or 46. In
> this case, 46. Hence I expected it to round up and the final answer to
> be 0.46.  It doesn't.
> 
> I'm confused!!  :-)

I

> 
> ---- Under Delph 7 I got this  -----------
> Failing on 9: Expected <0.00> but got <0.01>
> 
> Failing on 10: Expected <0.44> but got <0.45>
> ------------------  end  --------------------
> 
> So what rounding does Delphi 7 use?

No idea.

Vincent