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From: Marius Amado Alves <amado.alves@netcabo.pt>
Newsgroups: comp.lang.ada
Subject: Re: Float to String
Date: Wed, 10 Nov 2004 18:02:44 +0000
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Date: 2004-11-10T18:02:44+00:00

>>Float'Image (Float_Value)
>>and
>>Float'Value (String_Holding_The_Previous)
> 
> That's the problem, you loose quite a bit of precision with these convertions.

I just came across an example:

I have 64 bits available, so I define a 15 digits float

    type Float_64 is
       digits 15
       range -16#0.FFFF_FFFF_FFFF_F8#E+256
          ..  16#0.FFFF_FFFF_FFFF_F8#E+256;
    for Float_64'Size use 64;

Now I want to know the range in decimal (because the users will be 
inputing in decimal). I use 'Image on 'First and 'Last:

    First :-1.79769313486232E+308
    Last  : 1.79769313486232E+308

Now I rewrite the type definition to make it selfdocumenting:

    type Float_64 is
       digits 15
       range -1.79769313486232E+308
          ..  1.79769313486232E+308;
    for Float_64'Size use 64;

But now GNAT complaints that the size is too small, minimum allowed is 96!

Decrementing the last digit

       range -1.79769313486231E+308
          ..  1.79769313486231E+308;

makes it pass.

The culprit is probably the fact that approximations are in the 
direction away from zero.

And GNAT says 96 bits (and not 65) probably because of alignment 
requirements.

Anyway, just an illustration of how reconversions between systems (hexa 
and decimal) can be disruptive.