diff options
author | Markus Mützel <markus.muetzel@gmx.de> | 2022-08-04 13:55:17 +0300 |
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committer | Corinna Vinschen <corinna@vinschen.de> | 2022-08-04 13:55:17 +0300 |
commit | d939b16adc9d05d225970de1281684fa097565eb (patch) | |
tree | b064bd5191cfd9538fd5dca7a9ec493ef1e57f19 | |
parent | 70c7e8c1baaf5aa3a1e7327cd21463f4fa5b336b (diff) |
casinh: Use approximation for large input.
Signed-off-by: Martin Storsjö <martin@martin.st>
Signed-off-by: Corinna Vinschen <corinna@vinschen.de>
-rw-r--r-- | winsup/cygwin/math/casinh.def.h | 21 |
1 files changed, 21 insertions, 0 deletions
diff --git a/winsup/cygwin/math/casinh.def.h b/winsup/cygwin/math/casinh.def.h index 0cf46980d..3d04d483b 100644 --- a/winsup/cygwin/math/casinh.def.h +++ b/winsup/cygwin/math/casinh.def.h @@ -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; |