[Bug 216864] cpow(), cpowf(), and cpowl() need better implementations

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https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=216864

--- Comment #7 from Steve Kargl <kargl at FreeBSD.org> ---
(In reply to Ed Maste from comment #6)

> a. adding comments to those files referencing this PR (or
> a similar PR for other functions) and pointing out that a
> proper implementation is required

It can't hurt, but I suspect that I'm the only person 
besides bde that looks at the implementation details
of the various libm functions.

> b. adding a link-time warning (as emitted if using e.g.
> gets) that the current implementation is poor quality

To theraven@'s credit, he does have a link-time and/or
run-time warning in imprecise.c.  his code is

/*
 * If long double is not the same size as double, then these will lose
 * precision and we should emit a warning whenever something links against
 * them.
 */
#if (LDBL_MANT_DIG > 53)
#define WARN_IMPRECISE(x) \
        __warn_references(x, # x " has lower than advertised precision");
#else
#define WARN_IMPRECISE(x)
#endif

The message can probably be audited to state

 __warn_references(x, # x " needs a code review and tested");

and added to cpow[fl] and powl code.

> Is this an accurate view of the current status:
>
> Some sort of work in progress: ccoshl ccosl cexpl csinhl csinl
> Improved implementations needed: cpow cpowf cpowl powl tgammal
> No current implementation: ctanhl ctanl

ccoshl, ccosl, and cexpl are implemented.  I need to do more testing,
and the code needs review.  I post codes to freebsd-numerics@ and 
bde normal does a review.  At the moment, I have the feeling that I
am the only subscriber to that list.

csinhl and csinl will be implemented this week.  Review and testing
will follow.  I haven't looked at ctanh and ctan, so don't know the 
difficulty in porting those to ld80 and ld128.

tgammal is mapped by imprecises.c to tgamma, so at most 53-bit precision.

cpow[fl] and powl use Cephes.  These could use review and testing.
I suspect that bde will not look at this code, and I probably will
just work new implementations.

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