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
