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casinh: Use approximation for large input. 

Signed-off-by: Martin Storsjö <martin@martin.st>
Signed-off-by: Corinna Vinschen <corinna@vinschen.de>
This commit is contained in:
Markus Mützel 2022-08-04 12:55:17 +02:00 committed by Corinna Vinschen
parent 70c7e8c1ba
commit d939b16adc
1 changed files with 21 additions and 0 deletions
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21
winsup/cygwin/math/casinh.def.h
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@ -87,6 +87,27 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
if (r_class == FP_ZERO && i_class == FP_ZERO)
return z;
/* casinh(z) = log(z + sqrt(z*z + 1)) */
if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
|| __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
{
/* For large z, z + sqrt(z*z + 1) is approximately 2*z.
Use that approximation to avoid overflow when squaring.
Additionally, use symmetries to perform the calculation in the first
quadrant. */
__real__ x = __FLT_ABI(fabs) (__real__ z);
__imag__ x = __FLT_ABI(fabs) (__imag__ z);
x = __FLT_ABI(clog) (x);
__real__ x += M_LN2;
/* adjust signs for input quadrant */
__real__ ret = __FLT_ABI(copysign) (__real__ x, __real__ z);
__imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
return ret;
}
__real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) + __FLT_CST(1.0);
__imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;