On Sun, Oct 08, 2017 at 11:10:06PM +0200, Jan Stary wrote:
> On Oct 08 11:31:16, [email protected] wrote:
> > On Fri, Oct 06, 2017 at 02:12:01PM +0200, Jan Stary wrote:
> >
> > > Isn't "4 * a(1)" a more natural incarnation of pi than "2 * a(2^10000)"?
> >
> > The point of this example is to (also) show that a() works on very
> > large numbers.
>
> My itch is that 4 * a(1) _is_ pi, and the "approximation"
> is in how precisely you compute it; while 2 * a(2^10000)
> is _not_ pi, however precisely you compute it.
>
> Do you mean that a() _works_ in that it not only accepts
> the very large argument, but actually computes a sensible value?
> Unlike the other functions, arctg() has a limit at infinity.
>
> Interestingly, in bc.library, a() is the "basic" function
> approximated with (i)rational functions, and s() and c() are
> built on top of it (using a(1) of course :-), giving e.g.
>
> bc -l -e 'scale = 500; s(2^10000 * 4 * a(1))' -e quit
>
> around -.855 instead of zero. Indeed, it seems to be s() which
> has this problem, while a() gives a good approximation.
>
> So do you mean to illustrate that a() works with large arguments,
> _unlike_ e.g. s()?
>
> Jan
OK, OK, I'll change it.
-Otto
