Re: I vote NO on Motion P1788/M0024.02:RoundedOperations

[John Pryce <j.d.pryce@xxxxxxxxxxxx>]

Michel & All

On 16 May 2011, at 16:49, Michel Hack wrote:
> P.S.  When it comes to applying this notion to transcendental functions
>      we'll run into some difficulties, even when requiring no more than
>      reasonably-tight inclusion:  what to do for functions like arctan()
>      where the mathematical endpoint may not be representable, and the
>      required outward rounding would lead to a range trespass?

Maybe I shouldn't re-rouse another hare, but I'm rewriting Juergen's Level 1 elementary functions and am minded to edit the recommended functions according to my prejudices. Michel's comment reminds me that I think

   arctanPi(x) = arctan(x)/Pi

is a more important candidate for inclusion than the current sin3(x) = 3(sin(x) - x)/x^3. Along with its inverse

   tanPi(x) = tan(Pi*x).

And their relatives derived from from cos and sin and atan2.

(Pi may not be the best multiplier. Pi/3 has some sense, so that we can enclose sin(Pi/6)=0.5 exactly along with tan(Pi/4) and cos(Pi/3).)

John