Fix tanf underflow close to pi/4 (bug 14154)

[Andreas Jaeger]

On 07/06/2012 09:25 PM, Joseph S. Myers wrote:
> Bug 14154 is a spurious underflow exception from tanf on arguments
> very close to an odd multiple of pi/4.  Where x is the distance of the
> argument from an odd multiple of pi/4, the underflowing operation in
> __kernel_tanf is
>
>          r = y + z*(s*(r+v)+y);
>
> where z is x squared and s is x cubed, y is 0 and r+v is small enough
> that the multiple of the fifth power of x can underflow.  This patch
> fixes the spurious exception by using a linear approximation when the
> argument is close enough to pi/4 for the higher-order terms to be <
> 0.5ulp of the result.  The tests added are the closest binary values
> above and below pi/4 and -pi/4, for each number of bits from 8 to 24,
> to provide coverage of a range of values close to pi/4 and -pi/4.
>
> Tested x86 and x86_64 and ulps updated accordingly.  (My testing did
> not show any need to update any ulps on x86_64.)
Ok, thanks,

Andreas
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