Re: conversions between fixed-point types

["John B. Matthews" <nospam@nospam.invalid>]

In article <h94obl$c7h$1@news.albasani.net>,
 Dirk Herrmann <fight_spam@invalid.invalid> wrote:

> Dirk Herrmann wrote:
> >> And, while experimenting and trying out Adam Beneschan's solution 
> >> for rounding (thanks for your answer, Alan) I got totally confused 
> >> because of the following code (I am using GNAT 4.3.4 with the 
> >> following command line options: gnatmake -f -gnatVa -gnata 
> >> -gnatwadhl.o -save-temps conversion.adb):
> > [...]
> >> Is this confusing behaviour allowed?  I will submit a bug report if 
> >> some expert confirms it is a GNAT bug.
> 
> John B. Matthews wrote:
> > I'm no expert, and I had some trouble following the conversions in 
> > your example.  [...]
> 
> Sorry, I should have given more details about why I am confused.

Not at all. My confusion arises from my own poor understanding of how to 
apply the rules to the various conversions.

> In particular I am disturbed by the fact that the following two lines produce 
> different results with GNAT, as has been confirmed for GNAT 3.15p (thanks, 
> tmoran):
>   FIO.Put(Float(FpB(Float(-1.5)))); TIO.Put(" ");      --> -1.20000E+00
>   FIO.Put(Float(MakeB(-1.5))); TIO.Put(" ");           --> -1.60000E+00
> In the first line, the conversion to FpB is done from a Float value, 
> which is a direct cast from -1.5.  In the second line, the conversion 
> to FpB is also done from a Float value, but in this case -1.5 is 
> passed as a Float argument to MakeB.  What I don't understand is, why 
> it should make a difference whether I cast -1.5 to Float and then 
> convert it to FpB compared to the situation where -1.5 is converted 
> to a Float argument, which is then converted to FpB.

I see what you mean. Here's my understanding: The Ada Reference Manual 
[1], section 3.6(32) on numeric type conversion refers to section G.2.1 
and G.2.3 for floating- and fixed-point arithmetic, respectively. The 
value -1.5 is exactly representable as type Float, but not as type FpB. 
The conversion to FpB is governed by G.2.3(10), so both -1.2 and -1.6 
are in the close result set. Because FpB is an ordinary fixed point 
type, rather than a decimal fixed point type, there's no requirement to 
prefer one element of the result set over another. The conversion back 
to Float is discussed in G.2.1(10). Because small is not a power of 
T'Machine_Radix, the result is implementation defined. I'm not sure if 
GNAT fully implements Annex G, and I may be overlooking something 
obvious.

From another perspective, I'm curious to know why the conversions are 
needed.

[1]<http://www.adaic.com/standards/05rm/html/RM-TTL.html>

[...]
-- 
John B. Matthews
trashgod at gmail dot com
<http://sites.google.com/site/drjohnbmatthews>