Fix casinh, casin overflow (bug 14996)

[Andreas Jaeger]

On 01/05/2013 01:33 AM, Joseph S. Myers wrote:
> Bug 14996 is spurious overflow of casinh (and so of casin) for large
> arguments, when the internal squaring of the argument overflows.
>
> In the calculation of z + sqrt (1 + z*z), for z in the first quadrant,
> 1 + z*z differs negligibly from z*z (in both modulus and argument) and
> so the value (of which the log is taken) differs negligibly from 2*z,
> if the modulus of z*z is of the order of 1/epsilon or larger.  In this
> patch, 1/epsilon is actually used as a threshold on the real and
> imaginary parts of z to choose a simpler calculation, since the
> epsilon value is conveniently available as a constant whereas
> sqrt(epsilon), approximately the least threshold that could be used,
> isn't.  (Any value whose order of magnitude is between sqrt(epsilon)
> and sqrt(max representable value) would be a suitable threshold,
> though values close to either end of that range would need more
> careful consideration of what exactly the bounds are.)
>
> Tested x86_64 and x86 and ulps updated accordingly.

Thanks, this is fine,

Andreas
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