Re: understanding floating point types

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On Sun, 22 Aug 2010 03:37:35 -0700 (PDT), Ada novice wrote:

> On Aug 22, 11:51�am, "Dmitry A. Kazakov" <mail...@dmitry-kazakov.de>
> wrote:
>> Compare:
>>
>> � �type My_Float is digits 1;
>>
>> My_Float'Machine_Mantissa = 24 (32-bit IEEE 754 is used to model it)
>> My_Float'Mantissa = 5 (= 4+1)
>>
>> � �type My_Float is digits 2;
>>
>> My_Float'Machine_Mantissa = 24 (32-bit IEEE 754 is used to model it)
>> My_Float'Mantissa = 8 (= 7+1)
> 
> Thanks. The Float'Machine_Mantissa remains constant in your examples
> with 1 and 2 precision digits. Is the Float'Machine_Mantissa a
> predefined value that is constant for any precision digit requested?

No, it is the is best fitting machine number available (compiler's choice):

 � type My_Float is digits 7;

   My_Float'Machine_Mantissa = 53 (64-bit IEEE 754 is used to model it)
   My_Float'Mantissa = 25

> I have a second query: Say we consider the type My_Float is digits 2.
> This means that between the model numbers, the resolution is 1/(2^8)
> with the 8 in the expression obtained as 4 X 2. Am I right? Now if we
> have to multiply two numbers: say a = 2.33 and b = 3.45. Does Ada
> first convert each operation to its nearest model number and then do
> the multiplication and represent the result to its nearest model
> number? Or does Ada do the multiplication first and then represent the
> result to to its nearest model number?

I would expect that all computations performed in machine numbers, not
because it is mandated, I believe it is not, but because it is simpler to
implement. At least with GNAT it is so. Try this:

   type My_Float is digits 2;
   X : My_Float := 1.0 / 3.0;
   ...
   Put_Line (Float'Image (Float (X)));

The output will be: 3.33333E-01

If you can pick any number from the interval [0.33, 0.34[ to represent 1/3
in with 2 decimal digits. Why not 0.333333?

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