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Re: Balance

Gabriel Dos Reis schrieb:

On Sat, Nov 15, 2008 at 4:00 AM, Ulrich Kulisch
<Ulrich.Kulisch@xxxxxxxxxxx> wrote:


I am deeply convinced that a future interval arithmetic standard must
require hardware support for interval arithmetic. If we do not explicitely
require this we will not get it.


I agree with almost everything you said, except this one which is very
puzzling to me.
I'm making the assumption that ultimately, the interval standard is going to
be made concretely available in some concrete programming languages.
If so, what are the means to very that the interval standard indeed has
a hardware support?

-- Gaby


Dear Gaby:
Thank you for your mail. I am sorry for the delay. Let me try to answer your question.
On all existing processors interval operations are slower by magnitudes than the corresponding floating-point operations. This is the great hindrance to a wider acceptance. The main reasons why software simulations of interval arithmetic are slow are the case selections for interval multiplication (9 cases) and for division (14 cases) and the simulation and frequent changes of the rounding mode.
Now take a look at the many mails we are getting every day. Many of them are trying to gain speed by defining operations between floating-point numbers and intervals. This causes very complicated and perhaps even unsolvable questions (how to handle the IEEE P754 exceptions, etc.). Floating-point arithmetic and interval arithmetic are different calculi to approximate arithmetic for real numbers.
Let us assume now that we have a processor that can perform every interval operation about as fast as the corresponding floating-point operation. Then the need to combine the two calculi does not exist anymore. This would greatly simplify the development of an interval arithmetic standard.
In my paper with Reinhard Kirchner (I attach a copy) we show that on most processors on the market (Intel and AMD x86 processors) interval arithmetic can be made about as fast as simple floating-point arithmetic with very very little additional hardware costs. I am convinced that we would get this if the scientific computing community would require it loud enough. 

Bet wishes
Ulrich

Attachment: paper.pdf
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