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cacosh: 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 12:55:52 +02:00 committed by Corinna Vinschen
parent d939b16adc
commit ab31794e8a
1 changed files with 21 additions and 0 deletions
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21
winsup/cygwin/math/cacosh.def.h
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@ -80,6 +80,27 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z)
return ret; return ret;
} }
/* cacosh(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 positive
half plane. */
__real__ x = __real__ z;
__imag__ x = __FLT_ABI(fabs) (__imag__ z);
x = __FLT_ABI(clog) (x);
__real__ x += M_LN2;
/* adjust signs for input */
__real__ ret = __real__ x;
__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); __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) - __FLT_CST(1.0);
__imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z; __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;