Rounding with decimal types

Rounding with decimal types

[Wiktor Moskwa]

Hello,

I'm trying to understand how rounding in Ada 95 decimal types works.
Reference manual is unfortunately not clear to me on this subject.
I declare a decimal type and few variables:

type My_Decimal is delta 0.01 digits 18;
A, B, C : My_Decimal;

I want to have full control over rounding after multiplication and
division. Let me post two examples:

A := 0.01;
B := 0.50;
C := My_Decimal (A * B);	-- now C = 0.00

A := 0.01;
B := 0.50;
C := My_Decimal'Round (A * B);	-- now C = 0.01

So in the former example the result is truncated towards 0 and
in the latter it is rounded away from 0 when the result lies
between two integers. 
That's OK, but is it all that I can do with decimal numbers? 
How can I round up, down (explicitly) or perform "banker's rounding"?
Unfortunately 'Floor 'Ceiling and 'Unbiased_Rounding seem to work only
for floating point types.

The problem that I'm trying to solve is what type is best suited
for financial arithmetic and money representation.

Thanks for your help.

-- 
Wiktor Moskwa

Re: Rounding with decimal types

[Wiktor Moskwa]

On 25.11.2007, Dennis Lee Bieber <wlfraed@ix.netcom.com> wrote:
> On Sun, 25 Nov 2007 15:36:39 +0000 (UTC), Wiktor Moskwa
><wiktorDOTmoskwa@gmail.com> declaimed the following in comp.lang.ada:
>
>> The problem that I'm trying to solve is what type is best suited
>> for financial arithmetic and money representation.
>>
> 	For this, I'd suggest you define your data type to carry at least
> one decimal place more significance than the monetary unit normally
> supports. That gives you a guard digit on which to apply your own
> rounding algorithm for display (you should probably NOT round values
> that will be used for continued computation -- only round the display
> representation).

Hi Dennis,

Thanks for your hint but I'm only trying to use a tool which is decimal type
in Ada. Guard digit and extended precision would be a good idea if we needed
the best possible accuracy but if the process of computation is well defined 
including what method of rounding to use in which step, extra precision 
would be erroneus.

I'd like to know if there is "round up" and "unbiased rounding"
implemented for decimal types in Ada and if not, how "is it usually done"?
Thank you.

-- 
Wiktor Moskwa

Rounding with decimal types

[Grein, Christoph (Fa. ESG)]

For some information about decimal fixed point types and their
differences to ordinary fixed point types, see

http://en.wikibooks.org/wiki/Ada_Programming/Types/delta


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Re: Rounding with decimal types

[Dmitry A. Kazakov]

On Mon, 26 Nov 2007 08:15:02 +0000 (UTC), Wiktor Moskwa wrote:

> I'd like to know if there is "round up" and "unbiased rounding"
> implemented for decimal types in Ada and if not, how "is it usually done"?

Yep, this is a problem, I faced it too but for floating-point numbers when
implemented interval computations. There one needs rounding up and down as
well.

I would suggest something as clumsy as:

   -- Up-rounding multiplication
function "*" (Left, Right : My_Decimal) return My_Decimal is
   type Impl is new My_Decimal;
begin
   if Left = 0.0 then
      return 0.0;
   else
      declare
         Result : Impl := Impl'(Impl (Left) * Impl (Right));
      begin
         if Result / Left /= Right then
            return My_Decimal'Succ (My_Decimal (Result));
         else
            return My_Decimal (Result);
         end if;
      end;
   end if;
end "*";

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de

Re: Rounding with decimal types

[Wiktor Moskwa]

On 26.11.2007, Grein, Christoph (Fa. ESG) <Christoph.Grein@eurocopter.com> wrote:
> For some information about decimal fixed point types and their
> differences to ordinary fixed point types, see
>
> http://en.wikibooks.org/wiki/Ada_Programming/Types/delta
>

This page of Ada wikibook was one of the first places that I visited :-)
But thanks anyway.

-- 
Wiktor Moskwa

Re: Rounding with decimal types

[Wiktor Moskwa]

On 26.11.2007, Dmitry A. Kazakov <mailbox@dmitry-kazakov.de> wrote:
> On Mon, 26 Nov 2007 08:15:02 +0000 (UTC), Wiktor Moskwa wrote:
>
>> I'd like to know if there is "round up" and "unbiased rounding"
>> implemented for decimal types in Ada and if not, how "is it usually done"?
>
> Yep, this is a problem, I faced it too but for floating-point numbers when
> implemented interval computations. There one needs rounding up and down as
> well.
>
> I would suggest something as clumsy as:
> [..]

I've almost forgotten about operator overloading in Ada (too much
Java coding...) - thanks for reminding :)

-- 
Wiktor Moskwa