RE: Floating point related question

Peter,

Thanks for your reply.  I agree fully, the magnitude of the error
will change depending on the equations, but that shouldn't make the
"eps" function less useful.  One just has to propagate the error
through the equations rigorously and arrive to the maximum possible
error that way.  Of course the better way would be if the tools
or compilers could take care of this automatically...  Is that
wishful thinking?  I should have told Santa when he came... :-)

I would highly recommend to add an "eps" compatible function to
VHDL-AMS.  Would this have to be a language feature, or can it
be provided in a standard library of some sort?

Thanks,

Arpad
===================================================================

-----Original Message-----
From: Peter Ashenden [mailto:peter@ashenden.com.au] 
Sent: Wednesday, December 20, 2006 5:21 PM
To: Muranyi, Arpad; vhdl-ams@server.vhdl.org
Subject: RE: Floating point related question

Arpad,

That's a really good question. Currently, there is no such function. As of
VHDL-2002 (and hence VHDL-AMS-2007), floating point numbers have to be IEEE
double precision or better. So it would be feasible to define a function
similar to Matlab's eps function, assuming double precision representation.
Might be worth raising it as a requirement for both VHDL and VHDL-AMS.

A further issue comes to mind. If you're doing numerical computation, you
accumulate error, the magnitude of which depends on the behavior of the
algorithm. That means a final result may have greater than eps error
compared to some expected value. For example, if you do

  assert abs(computation(x) - expected_x) < eps;

the accumulated error might mean that the result of the computation is more
than eps away from expected_x, even though the computation has been
performed correctly. Knowing what value to use in place of eps (or how much
to scale eps) involves numerical analysis of the computation. Does this make
a putative eps function less useful in practice?

Cheers,

PA
--
Dr. Peter J. Ashenden         peter@ashenden.com.au
Ashenden Designs Pty. Ltd.    www.ashenden.com.au
PO Box 640                    VoIP: sip://0871270078@sip.internode.on.net
Stirling, SA 5152             Phone (mobile):  +61 414 70 9106
Australia


> -----Original Message-----
> From: owner-vhdl-ams@server.eda.org 
> [mailto:owner-vhdl-ams@server.eda.org] On Behalf Of Muranyi, Arpad
> Sent: Thursday, 21 December 2006 10:39 AM
> To: vhdl-ams@server.vhdl.org
> Subject: Floating point related question
> 
> 
> Hello Everyone,
> 
> We all know that using relational operators between
> floating point numbers is a risky proposition.  This
> code, for example, may never execute, believe it or
> not, (I tried it):
> 
>       if (0.1+0.2 = 0.3) then
>         report "Test";
>       end if;
> 
> However, there are times when taking care of such
> floating point errors may be needed.
> 
> In Matlab there is a function, called "eps" which
> can help in incorporating such errors in equations. 
> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/inde
x.html?/ac
cess/helpdesk/help/techdoc/ref/eps.html&http://www.google.com/search?hl=
en&q=eps+function

I would like to find out whether there is a similar
function in VHDL-AMS.  For a moment I thought I could
use the T'succ(x) or related functions, but the problem
is that this would only work on discrete or physical
types.  The type "real" is not one of these.  Could
someone give me some ideas how to go about this?

Thanks, and Happy Holidays...

Arpad
========================================================