Stavros Macrakis wrote:
>
>
>
> To get sinh(1.0b-10) correct to 16 places, you need fpprec=25, and to
> get sinh(1.0b-2000) correct to 16 places, you need fpprec=2015. That
> doesn't seem like a practical solution to me....
>
> -s
>
As long as you can compute the number of extra digits of precision,
then this is not only feasible, it is pretty much inevitable.
Finding n decimal digits (relative error less than 10^-n) near
a zero of the underlying function, usually requires bumping
up the precision considerably. Like sin() near 1000000*pi.
Or bessel functions near one of the zeros.
The only question is how to have the system do this rather than
the user (bump up the precision). Of course some formulas could
probably be revised for better accuracy and consistent branches.
Since the CL branch choices were mostly or entirely those
suggested by W. Kahan here at Berkeley, and I haven't heard
him alter his views on this, I think they are probably better
than alternatives. Some of those may have come from
the Abramowitz and Stegun Handbook, but may not survive the
next version (see dlmf.nist.gov).
RJF