Re: Little Endian -> Big Endian (Ada95 / GNAT), Whats with floating point types?

["Warren W. Gay VE3WWG" <warren@ve3wwg.tk>]

Hyman Rosen wrote:

> Warren W. Gay VE3WWG wrote:
>> you can still represent a machine dependant number with
>  > repeating decimal places
> 
> There are no such numbers (on any common hardware). 

Because I am not in a position here and now to
say "here is one", all I can do is say "I _think_ you're
incorrect about this". I seem to recall one or more
machine formats that keep one bit of state that says
this is a repeating digit (perhaps I am thinking of
a FPU register, but I do know that I have seen
it somewhere).

> Whether
> it's IEEE, VAX, or any of a variety of other forms of hardware
> floating point representation, all of them can be written
> exactly as a finite length decimal number (not counting the
> bit patterns which do not represent numbers, of course).

So lacking any representation sources at the moment, are you
saying that there is absolutely no bit that indicates that
a digit repeats?  I am not sure that you are wrong - but I
seem to recall differently.  Perhaps, someone can provide
the relevant details.

>> If they don't do that, then the number has been rounded,
>> and thus does not quite represent the original value any
>> more ;-)   (at a minimum, it is less faithful than it
>> could be).
> 
> The OP was converting out of and back into the same representation.
> Given that, there are a pair of published algorithms which ensure
> completely faithful translation. 

And one such piece of information might be that the digit
repeats (1 bit, unless a group repeats).

> One algoritm takes a decimal
> representation and converts it to the binary representation closest
> in value (coin flip for ties) and the other finds a shortest decimal
> representation for a binary number which will convert back exactly to
> that binary.

None of that is new to me ;-)

> The algorithms were both published in Proceedings of the ACM SIGPLAN
> '90 Conference on Programming Language Design and Implementation.
> 
>     G. L. Steele Jr. and J. L. White.
>     How to Print Floating Point Numbers Accurately.
> 
>     W. D. Clinger
>     How to Read Floating Point Numbers Accurately
> 
> You can find free implementations of these algorithms in C at
> <http://www.netlib.org/fp/>.

Can you point me/us to an online IEEE format description? I'd
like to check my memory for parity errors ;-)

-- 
Warren W. Gay VE3WWG
http://ve3wwg.tk