(j3.2006) Liaison to IFIP WG 2.5

[keith bierman]

On Aug 21, 2007, at 5:06 PM, Van Snyder wrote:

>
>
> Modules are actually not an adequate foundation for serious interval
> computations, given the way Fortran provides support for directed
> roundings.  The problem is compounded by the way Intel


Don't pick on Intel. That's pretty much the way everyone does it  
(alpha didn't ... except for one mode ;<). If interval methods become  
widely used, it's likely that this could be somewhat minimized  
(without ISA changes). But it's pretty nontrivial. Easier if you have  
a new ISA and you put *ALL* the roundings as static encodings ;>

...

> unit, 100X overhead compared to point arithmetic is not uncommon  
> and not
> unexpected.

That's doing things naively. If you are clever you can do rafts of  
computation with one rounding mode, and then change the mode and do  
the next set. All the moreso with enough cores to be working in  
parallel. Of course, then it is intractable if it's just modules,  
hand code, and an optimizer stuck trying to paste it all back together.
> ...
> The history of mathematical software is the provision of carefully
> written computational kernels for narrowly-specified mathematical
> operations (such as FFT or zero finding).  These, and the user- 
> provided
> code they frequently need, not entire applications, are where interval
> arithmetic would be used.

It's a big enough paradigm shift that I don't think it's entirely  
unlikely that entire applications (well, the floating point parts)  
would be coded the new way. But because it's such a big shift getting  
folks to do it at all is a very tough problem.

CS students think the halting problem is hard. Computer Engineers in  
the field know that causing a computer to halt is easy (remove the  
power, drive a screwdriver through each and every CPU, etc.).

It's the *starting* problem where you need an entirely new platform  
(ISA, compilers, applications, OS, etc.) that is nearly intractable.   
Of course, that's a job for Venture Capitalists ;>


---
Keith H. Bierman   khbkhb at gmail.com
<speaking for myself*> Copyright 2007