Re: New approach to annex D of the 754-R proposal.

[Peter Henderson <petercbh@xxxxxxxxxxx>]

Florent de Dinechin wrote:
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> 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...
I apologise, but I can't resist.  tanPi(-1/2) must equal -infty, 
tanPi(+1/2) must equal +infty and cotPi(1) must equal -infty.  This is 
because nobody would accept anything other than atanPi(tanPi(x)) = x for 
x in [-1/2, +1/2] and tanPi(atanPi(x)) = x in [-infty, +infty], 
similarly for cotPi and acotPi.  How the signs are assigned for the 
remaining inifinities depends on the signs assigned to the zeros of 
sinPi and cosPi.  The assignment in the proposed standard of +0 for both 
sinPi and cosPi when x is > 0 means the signs of the infinities of tanPi 
and cosPi will alternate starting from the values above.

Regards,
Peter Henderson