Re: Fixed point constants issue

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

On Mon, 13 Sep 2010 20:25:43 +0200, Vinzent Hoefler wrote:

> On Mon, 13 Sep 2010 20:04:32 +0200, Dmitry A. Kazakov  
> <mailbox@dmitry-kazakov.de> wrote:
> 
>> On Mon, 13 Sep 2010 19:27:30 +0200, Vinzent Hoefler wrote:
>>
>>> Is this a GNAT bug or am I just stupid?
>>>
>>> Suppose we have a fixed point type (with a rather large delta):
>>>
>>> -- 8< --
>>> with Ada.Text_IO; use Ada.Text_IO;
>>>
>>> procedure Fixed_Point
>>> is
>>>     FEET_PER_METER : constant := 0.3048;
>>>     HEIGHT         : constant := 10; -- Feet
>>>
>>>    type Altitude is delta (2.0**15 / 50_000.0) range 0.0 .. 50_000.0;
>>
>> [...]
>>> Can anyone shed some light on this? This has driven us crazy for weeks  
>>> now.
>>>
>>> [1] Of course, "Altitude'(HEIGHT * FEET_PER_METER)" yields "0.0" again.
>>>      At least this is consistent with my understanding so far.
>>
>> Hmm, what did you expect? 0.3048 (FEET_PER_METER) is 0 when Altitude.  
>> That is because 2.0**15/50_000.0=0.65536 > 0.3048.
> 
> Yes, of course. Still, it's not quite intuitive why
> 
>   TEN_FEET_1 : constant          := HEIGHT * FEET_PER_METER;
>   TEN_FEET_2 : constant Altitude := HEIGHT * FEET_PER_METER;
> 
> just because a type is given in the second case.

Different types, different behavior.

> I would expect the compiler to evaluate the expression "HEIGHT *  
> FEET_PER_METER" _before_ converting it to the appropriate fixed point type.

Why? "*" is defined on Altitude. You should rather wonder why the result is
different for TEN_FEET_4. Multiplication is inexact taking rounding this or
that way you get different results.

> And, obviously it does this that when evaluating
> 
>    TEN_FEET_4 : constant Altitude := Altitude (HEIGHT * FEET_PER_METER);

Well, it does not, because here another type is involved.

But what about:

   X : constant Altitude := 0.3048; -- The result is 0

Does it wonder you? You should consider fixed point values intervals. So 0
is actually something like [0, 0.65536[. When multiplied to 10 it becomes
[0, 6.5536[. That thing has 10 intervals of 0.65536 width in it. "0"=[0,
0.65536[ and "3"=[3.048, 3.70336[ are just two of them. The choice is more
or less arbitrary.

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