From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: by sourceware.org (Postfix, from userid 2155) id 41047385802E; Thu, 4 Aug 2022 10:56:47 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org 41047385802E Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: quoted-printable From: Corinna Vinschen To: cygwin-cvs@sourceware.org Subject: [newlib-cygwin] cacosh: Use approximation for large input. X-Act-Checkin: newlib-cygwin X-Git-Author: =?utf-8?q?Markus_M=C3=BCtzel?= X-Git-Refname: refs/heads/master X-Git-Oldrev: d939b16adc9d05d225970de1281684fa097565eb X-Git-Newrev: ab31794e8a1da13224eca78b58df9a72d78fb6ae Message-Id: <20220804105647.41047385802E@sourceware.org> Date: Thu, 4 Aug 2022 10:56:47 +0000 (GMT) X-BeenThere: cygwin-cvs@cygwin.com X-Mailman-Version: 2.1.29 Precedence: list List-Id: Cygwin core component git logs List-Unsubscribe: , List-Archive: List-Help: List-Subscribe: , X-List-Received-Date: Thu, 04 Aug 2022 10:56:47 -0000 https://sourceware.org/git/gitweb.cgi?p=3Dnewlib-cygwin.git;h=3Dab31794e8a1= da13224eca78b58df9a72d78fb6ae commit ab31794e8a1da13224eca78b58df9a72d78fb6ae Author: Markus M=C3=BCtzel Date: Thu Aug 4 12:55:52 2022 +0200 cacosh: Use approximation for large input. =20 Signed-off-by: Martin Storsj=C3=B6 Signed-off-by: Corinna Vinschen Diff: --- 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.de= f.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; } =20 + /* cacosh(z) =3D log(z + sqrt(z*z - 1)) */ + + if (__FLT_ABI(fabs) (__real__ z) >=3D __FLT_CST(1.0)/__FLT_EPSILON + || __FLT_ABI(fabs) (__imag__ z) >=3D __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 =3D __real__ z; + __imag__ x =3D __FLT_ABI(fabs) (__imag__ z); + x =3D __FLT_ABI(clog) (x); + __real__ x +=3D M_LN2; + + /* adjust signs for input */ + __real__ ret =3D __real__ x; + __imag__ ret =3D __FLT_ABI(copysign) (__imag__ x, __imag__ z); + + return ret; + } + __real__ x =3D (__real__ z - __imag__ z) * (__real__ z + __imag__ z) - _= _FLT_CST(1.0); __imag__ x =3D __FLT_CST(2.0) * __real__ z * __imag__ z;