Re: Please listen to Ulrich here...

[Richard Fateman <fateman@xxxxxxxxx>]

On 8/25/2013 9:10 AM, Ulrich Kulisch wrote:

Am 24.08.2013 20:13, schrieb Richard Fateman:

On 8/23/2013 9:58 PM, Ulrich Kulisch wrote:

Ian,

I attach a few more pages which might be interesting for you.

Best regards
Ulrich

P.S.: These details are more or less known since 1980. But obviously
they are not wide spread. I discussed this matter already with
IEEE754R. At the end they said they don't have the necessary knowledge
to make a clear decision. A few month after the first edition of my
book was published in 2008 IEEE 1788 was founded. Now it seems that we
end with the same situation.

Repeatedly pointing out the hardware aspects makes me wonder if the argument
for EDP being essential for interval computation other than EDP of
intervals is simply
unsupported.

RJF

I don't quite understand this mail. An EDP for intervals, of course, is supported. Section 7.5.2 of my book (second edition).

I agree that you don't understand this mail!

Let us say that there was some debate about whether or not an interval hyperbolic cosine  (cosh) should be
required as part of the standard.  Would repeated presentations of how to compute scalar
cosh in hardware or using an FPGA affect your opinion as to whether cosh should be
required in the interval standard?  I think not.  You might wish to argue

(a) cosh is important in existing applications.
(b) cosh is standardly available in numerical scalar libraries and
so if someone were to attempt to routinely upgrade a computation
already part of a scalar program to an interval program, it would be needed.
(c) the best method for computing interval cosh is different from any obvious
  way of computing cosh.  Here are obvious way, but is it good?:
   cosh(x):= 1/2*(exp(x)-exp(-x)).
here's another one:
   cosh(x):= 1/2*(exp(-2*x))*(exp(2*x)+1)
here's another one:
cosh(x):=  1+x^2/2+x^4/24+....
  ... that last method looks good to me if 1+x^2/2 is indistinguishable from 1.



(d) cosh can be computed by FPGA??  This is, in my opinion, irrelevant.




Similarly, for EDP: either it is deemed fundamental to any interval system and should be required,
or not.

Whether it can be implemented in hardware is irrelevant in answer to this question.
This seems to be the point which is eluding you.  Please don't say "read my book".

If EDP is the best or only way to compute something deemed fundamental to the interval
standard, then it has not been explained or defended,  at least recently. 

 If EDP is an appendage to the standard that only pertains to EDP of intervals,  and EDP of intervals can be computed in software or hardware, it is of no merit to argue that it can be computed in hardware.

Just as it would not be particularly supportive to argue that cosh MUST be in 1788 standard
because can be implemented in FPGA or hardware, or by table lookup etc.  

RJF

Regards
Ulrich