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From: Guillaume Melquiond (guillaume.melquiond_at_[hidden])
Date: 20051208 06:38:04
Le mercredi 07 décembre 2005 à 10:59 0500, David Abrahams a écrit :
> I find this in the documentation, which sounds selfcontradictory:
>
> > Unprotected rounding
>
> > As explained in this section, a good way to speed up computations
> > when the base type is a basic floatingpoint type is to unprotect
> > the intervals at the hot spots of the algorithm. This method is safe
> > and really an improvement for interval computations. But please
> > remember that any basic floatingpoint operation executed inside the
> > unprotection blocks will probably have an undefined behavior (but
> > only for the current thread).
>
> a. That doesn't sound "safe."
Indeed. This is the reason why it is not enabled for the whole program,
contrarily to what it is done in a few other interval libraries. This
can be restricted to a scope and the user has to explicitly enable it.
> 1. there's the potential undefined behavior.
As soon as you break the assumption other parts of a program make about
the rounding mode, you can lead them to invoke undefined behavior.
sin(double) can easily return a value that is not between 1 and 1, if
it is invoked in a scope where the rounding is not preserved.
> 2. there's the whole notion of "unprotect"ing the computation.
> Don't I lose the value of interval computation? That is, will
> my computed results still reflect the potential error due to
> floatingpoint precision limits?
The interval computations are fine. These are the floatingpoint
computations that are not.
> b. How am I going to do any useful computation in an unprotection
> block without doing any basic floatingpoint operations?
Interval computations are useful.
> If it's not selfcontradictory, could you explain what it means and,
> if possible, improve the wording?
>
> >From reading the docs, it's very unclear what optimization this
> unprotection mechanism allows, and it's unclear when/how it's
> mathematically valid to use the results (e.g. why not do all
> computations that way if it's faster?) I get only a vague sense of
> the answers to these questions from the docs. Yes, I read the Horner
> example.
Ideally, compilers should do this optimization themselves. Unfortunately
no compiler that I know does it. In fact, they are not even able to
properly handle the floatingpoint pragmas, so we are still years away
from the time they will do handle the optimization.
We cannot just tell the users: "in ten years, your compiler will
probably be able to optimize the code, you just have to wait till then,
before using the library". Please note that this problem plagues all the
interval libraries that do not benefit from dedicated compiler support
(like the one the Sun compiler provides).
So, in the meantime, we have provided a way for the user to emulate this
optimization by manually deciding of program scopes where the rounding
mode is not changed and restored at each interval computation. The code
can get a few orders of magnitude faster, if it does intensive interval
computations.
> Finally, the use of the term "unprotection block" looks extremely
> misleading. It looks like you have unprotected datatypes, but "block"
> implies that there's a lexical scope within which unprotection is in
> effect. There does seem to be such a notion for rounding mode (by
> declaring an auto variable of I::traits_type::rounding), but not so
> for unprotect. Unless I'm gravely confused, which is possible, in
> which case, again, the docs need to be upgraded.
I agree the documentation should be clearer. As long as the variable of
type I::traits_type::rounding is alive, then we are in a scope that is
protected. In such a scope, floatingpoint computations will have
strange behaviors, but computations involving unprotected intervals
(they run a lot faster than computations involving correct intervals)
are able to give correct results.
Thanks to your comments, I now understand how speaking of "unprotected"
intervals can be misleading. By this term, we intended to express that
unprotected intervals lead to incorrect computations, when used outside
of a scope protected by a variable of type I::traits_type::rounding.
Best regards,
Guillaume
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