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

From: Hyman Rosen (hyrosen_at_mail.com)
Date: 03/04/04 

Date: Thu, 04 Mar 2004 13:34:41 -0500

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). 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).

> 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. 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.

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/>.

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