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Re: New approach to annex D of the 754-R proposal.
Vincent Lefevre a écrit :
On 2007-06-15 09:40:12 +0000, Michel Hack wrote:
Looks good. Some comments:
- tanpi x ]-infty,infty[ \ { 1/2 + k, k in Z}
I suppose the reason for excluding half-integers is that the sign of
Infinity would be undetermined by the limit argument. I wonder however
whether the rule used for the sign of x-x could not be used here: +Inf
except when rounding towards -Inf.
I don't think this would be a good idea. Note that one has +0 = -0 (so
that even if the sign of the zero is incorrect, one gets a value that
is equal to the "correct" value), but one does not have +inf = -inf.
So, the zeros and the infinities should not be treated in the same way.
I agree with Vincent. A general rule that handles such cases will be
much more difficult to justify.
However, if in some context you really had good reasons for that, an
alternative would be that a language defines (for example) the
mathematical function
tanpi x ]-infty,infty[ such that tanpi(1/2 + k, k in Z) = +infty
It is in anticipation of such situations that our proposal considers
mathematical functions as defined over the affinely extended reals with
values in the affinely extended reals.
Now I don't want to open an endless discussion on the choice of which
infinity, considering that tanpi is odd...
Florent