Re: As simple as it is now, I am still against motion 24.03...
On 2011-06-14 11:01:08 -0400, Michel Hack wrote:
> Vincent wrote:
> > Note that if x is a real, then [x,x] is a valid interval.
>
> At level 1 perhaps, but then we get into all that trouble about "exact"
> interval arithmetic that we discussed at length ove two years ago.
That's also true at Level 2, where x would then be a Level-2 real
number (i.e. a finite floating-point number).
The goal of my remark was the following: if we have a Level-2
interval function f, defining a Level-2 function from the
floating-point numbers to intervals would just be syntactic sugar,
as it may be seen as equivalent to the computations:
x -> [x,x] -> f([x,x])
since the first one (x -> [x,x]) is exact.
And I think the decomposition into x -> [x,x] and [x,x] -> f([x,x])
makes things less dangerous.
BTW, P1788 currently has:
* format-floatsToInterval(lo{x},hi{x}) to make the interval
[lo{x},hi{x}]
* format-floatToInterval(x) to make the interval [x,x]
I think the second form should be removed, as the user could still
write format-floatToInterval(x,x). IMHO, format-floatToInterval(x)
would be used mainly (only) when x is a basic constant, so that the
gain would just be a few characters. If x is a long expression (thus
probably with rounding errors), then format-floatToInterval(x) would
probably be incorrect because of these rounding errors.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)