Re: Motion 52: please hold
On 2013-11-20 10:17:19 +0000, John Pryce wrote:
> On 2013 Nov 19, at 14:08, John Pryce wrote:
> > Attached is the version of Clause 6 "Expressions" that I would
> > like voted on.
>
> Sorry, we need to hold up for a day or so.
>
> Vincent (2013 November 20 00:36) indicates he has been busy but
> wants to comment further on §6.1 when he has had some sleep!
Before going further, in the second item of §6.1:
"as defining various (depending on the finite precision interval
types used) interval functions that give proven enclosures for
the range of f over an input box x;"
one has the impression that the *only* purpose of an expression
is to define an interval function associated with f (a real point
function), while there are more general expressions (e.g. with
non arithmetic operations such as intersection). This is confusing.
To give an example, is intersection(a,b) an expression?
IMHO, it is an expression on intervals. Did you actually consider
arithmetic expressions? Or somethine more general?
In (c), I was complaining on "If the algebraic expression is evaluated
naively, such a subexpression is evaluated more than once, which
affects efficiency but not the numerics of what is computed." Compilers
has sub-expression elimination optimizations and so on. And when
identical subexpressions are evaluated several times, they may not
give the same result (as I have shown). You could talk of "different
versions" (I don't like that), but the only fact of writing the same
subexpression twice can imply different versions (and the user isn't
necessarily aware when this happens). So, I suggest to remove this
sentence. Is it really useful? Anyway the condition "the algebraic
expression is evaluated naively" almost never occurs in practice.
Similar problem with the new text about extended precision.
BTW, to give an example other than C, in Fortran, a+b+c can be
evaluated as (a+b)+c or a+(b+c), and possibly in other ways.
Note that x - x is still different from 0 on intervals (see discussion
above on what an expression is).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)