From ab31794e8a1da13224eca78b58df9a72d78fb6ae Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de> Date: Thu, 4 Aug 2022 12:55:52 +0200 Subject: [PATCH] cacosh: Use approximation for large input. MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Signed-off-by: Martin Storsjö <martin@martin.st> Signed-off-by: Corinna Vinschen <corinna@vinschen.de> --- winsup/cygwin/math/cacosh.def.h | 21 +++++++++++++++++++++ 1 file changed, 21 insertions(+) diff --git a/winsup/cygwin/math/cacosh.def.h b/winsup/cygwin/math/cacosh.def.h index 5105b426e..c2c2031eb 100644 --- a/winsup/cygwin/math/cacosh.def.h +++ b/winsup/cygwin/math/cacosh.def.h @@ -80,6 +80,27 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z) 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); __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;