[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[kreckel at ginac dot de]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

Richard B. Kreckel <kreckel at ginac dot de> changed:

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--- Comment #3 from Richard B. Kreckel <kreckel at ginac dot de> 2011-11-23 09:04:57 UTC ---
(In reply to comment #1)
> Created attachment 5740 [details]
> proposed patch for 2.13 release

That patch only fixes a symptom and not the cause. A better patch has been
attached to BZ 13305.

The rounding errors in cacosh[fl] are a completely different problem and should
be analyzed and fixed separately. They are due to the argument of the final
clog(y) being close to 1. The instability of log(1+x) for small x are
well-known and have lead to the log1p function. I believe the rounding errors
in cacosh[fl] would go away if the clog(y) would be replaced by clog1p(y), if
that would exist.

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