Re: Reasons (not) to vote Motion 27: NO
On 2011-08-19 19:18:44 +0200, Arnold Neumaier wrote:
> On 08/19/2011 06:51 PM, Vincent Lefevre wrote:
> >On 2011-08-19 16:44:38 +0200, Arnold Neumaier wrote:
> >>Decorations are a concept whose meaning is associated to the whole
> >>computation and its input and output, not to the single node in
> >>the dag, which only acts as an execution engine.
> >
> >Decorations should be specified on sub-DAGs only because the
> >implementation cannot know what occurs in the "whole computation".
> >Some information from the past is necessarily unknown to the
> >implementation.
>
> The implementation of the single operations needs to know nothing
> since it performs blindly according to the definition in Motion 26.
>
> But the user needs to know that decorations are informative only if
> the program written satisfies the assumptions of the FTDIA.
It seems that your point of view is based on the FTDIA, while I think
there should be a more powerful theorem that could be used to implement
new functions. Consider that you have an implementation that provides
the basic operations (+, -, *, /) and exp over the decorated intervals.
Then consider sinh(x) = (exp(x) - exp(-x)) / 2. It should be made clear
that one can implement sinh by using this formula (since sinh could
be used in expressions, x is here a decorated interval, unlike in the
FTDIA, and since the expression could contain other variables, e.g.
sinh(u/17) + v, one needs to make this work for a free expression),
i.e. it satisfies the propagation rule. For such a sinh implementation,
I regard x = u/17 as the input and sinh(x) as the output. The main
point is that: if p_d(f(u),u) holds, then p_d'(sinh(f(u)),u) holds,
where d is the decoration of x and d' is the output decoration of sinh.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)