Re: Proposed Level 1 text (less decorations)
On 2011-12-05 07:10:51 +0000, John Pryce wrote:
> P1788 members
>
> I circulate herewith a draft text, and submit a motion that it be
> accepted as text of the standard.
[...]
Not sure about the current status, but here are my comments:
General note: a rationale would help to understand some choices.
§3.1: Is the notation compatible with the ISO 80000-2:2009 standard?
http://en.wikipedia.org/wiki/ISO_31-11 says: R* = R \ {0}
§3.1, IR (editorial): } } -> }
§3.1, F: Must -inf and +inf be part of F?
§3.1, \overline{IF}: what about the empty set? (§5.2 gives an answer,
but "bounds" is not currently defined, and using infinite bounds for
the empty set is quite artificial).
§3.2.1 (arithmetic operation): "interval non-arithmetic operation" is
mentioned but not defined.
§3.2.6 (fma): "with only one rounding" -> This is Level 2!
§4.1: OK.
§5.5.1 (editorial): "2y" -> "(2y)"
§5.5.2: "The implementation's library contains all computable versions
of all provided arithmetic operations" -> What is meant by "all"?
§5.6, Table 2 page 17 (editorial):
* "R² \ {y = 0}" -> "R² \ (R × {0})" or "R × (R \ {0})"?
Similar change for pow(x,y)?
* The notation (x,y) is used with two different meanings: a set
(open interval) and an ordered pair. For sets, I suggest the
use of [x,y[, ]x,y] and ]x,y[.
* "case(b,g,h)" -> "case(c,g,h)" for consistency with §5.6.2.
Note e of Table 2: this is also true for exp and tanh.
§5.6.6, Table 4 page 19:
* I would prefer NaN for mid(x) on an unbounded interval, because
on non-Entire unbounded intervals, there are no centers of
symmetry, and for Entire, every real number is a center of
symmetry.
* What about mag(Empty) = -inf and mig(Empty) = +inf?
* I think that at Level 1, NaN could exist only as a result
and should be a synonym of "undefined".
§5.6.8 (dot product function): if the interval extension is not
required, this function shouldn't belong to §5.6.
§5.7.1, Table 5 page 20:
* Range of atanPi: [-1/2,1/2] -> (-1/2,1/2) or ]-1/2,1/2[.
* Domain of atan2Pi: (0,0) should be excluded (like for atan2).
§5.7.2, Table 6 page 21:
* Range of cosSlope2: [0,1] or (0,1]?
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)