Re: Transcendental function tables: comments welcome!

[Vincent Lefevre <vincent@xxxxxxxxxx>]

On 2007-05-28 22:27:36 +0000, Michel Hack wrote:
> Just a few minor points on Eric Postpischil's comments.
>
> > Notes for Table D.2 and Table D.3 define "n" as "Any nonzero
> > positive integer."  "Nonzero" is redundant (+0 notwithstanding).
>
> The standard addresses an international audience, and in some parts of
> the world "positive" includes zero ("strictly positive" does not, but
> sounds silly to the other parts of the world).  So let's be unambiguous.

Well, the standard is written in English. The meaning of "positive"
and "negative" in other languages doesn't matter. When zero is
included, it would be less unambiguous to say "positive or zero".

BTW, it is written in Draft 1.4.0:

  For f either of sinPi or tanPi, f(+n) is +0 and f(-n) is -0 for
  positive integer n. This gives us f(-x) = -f(x) for all x.
  cosPi(n + ½) = +0 for any integer n. This gives us f(-x) = f(x)
  for all x.

But +0 = -0. So, even if one chooses a different sign when the
result is 0, one would still have f(-x) = -f(x) (resp. f(-x) = f(x))
for all x. So, instead of "=", the standard should say "is" (or "is
equivalent to").

> Actually, I just realised that the CF expansion of pi or e is pretty
> irrelevant unless there is a partial convergent whose denominator
> is a power of the base -- which is highly unlikely, and probably has

I don't think so. You need to be close to a *multiple* of pi/2. But
you also need to take the exponent into account.

-- 
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)