Re: Floating-Point Numbers and Internal Representation

[Matthias Kretschmer <mccratch@gmx.net>]

On 2005-12-04, Dmitry A. Kazakov <mailbox@dmitry-kazakov.de> wrote:
> On Sun, 4 Dec 2005 16:15:31 +0100, Matthias Kretschmer wrote:
>
>> as I hope I said in my original posting, I am very well aware of this,
>> but I had this special case where I wanted to use explicitly equality.
>> There are times, when one is sure, that even with rounding errors, the
>> two compared floating point numbers are really equal or not if one is
>> using some good enough precision. So from some defined point on all
>> following digits can be considered garbage, as it was in my case.
>
> This is exactly definition of an interval: [xx.xxx0(0), xx.xxxx9(9)]
>
>> The
>> best solution would be that I had used Q (or a fixed subset of it)
>> instead an approximation of R for my calculations, but I was too lazy :)
>
> No, this contradicts to your statement about "following digits" being
> garbage. In the case of Q they are not.

ah well - as long as you know you have no periodical numbers, it doesn't
matter.

>
>> Maybe I should take the time and port it to such a solution or implement
>> something like that myself. At least in many circumstances using exact
>> numbers instead of unexact ones causes much less trouble :)
>
> Ah but this is a completely different story. If you *really* know that
> multiplication and division are exact then Ada's fixed point types is just
> what you need. Fixed point numbers are perfectly comparable.
>

hmm you're right. Forgot about this. Thanks for the hint. Didn't do
stuff in Ada for a long time, I think I forgot most of the stuff.

-- 
Matthias Kretschmer