From owner-freebsd-numerics@FreeBSD.ORG Sun Aug 12 23:12:38 2012 Return-Path: Delivered-To: freebsd-numerics@freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [69.147.83.52]) by hub.freebsd.org (Postfix) with ESMTP id 615921065675 for ; Sun, 12 Aug 2012 23:12:38 +0000 (UTC) (envelope-from peter@rulingia.com) Received: from vps.rulingia.com (host-122-100-2-194.octopus.com.au [122.100.2.194]) by mx1.freebsd.org (Postfix) with ESMTP id EE4AA8FC15 for ; Sun, 12 Aug 2012 23:12:37 +0000 (UTC) Received: from server.rulingia.com (c220-239-249-137.belrs5.nsw.optusnet.com.au [220.239.249.137]) by vps.rulingia.com (8.14.5/8.14.5) with ESMTP id q7CNCbHf075922 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=OK) for ; Mon, 13 Aug 2012 09:12:37 +1000 (EST) (envelope-from peter@rulingia.com) X-Bogosity: Ham, spamicity=0.000000 Received: from server.rulingia.com (localhost.rulingia.com [127.0.0.1]) by server.rulingia.com (8.14.5/8.14.5) with ESMTP id q7CNCVi8021821 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Mon, 13 Aug 2012 09:12:31 +1000 (EST) (envelope-from peter@server.rulingia.com) Received: (from peter@localhost) by server.rulingia.com (8.14.5/8.14.5/Submit) id q7CNCVQe021820 for freebsd-numerics@freebsd.org; Mon, 13 Aug 2012 09:12:31 +1000 (EST) (envelope-from peter) Resent-From: Peter Jeremy Resent-Date: Mon, 13 Aug 2012 09:12:31 +1000 Resent-Message-ID: <20120812231231.GT20453@server.rulingia.com> Resent-To: freebsd-numerics@freebsd.org Received: from vps.rulingia.com (host-122-100-2-194.octopus.com.au [122.100.2.194]) by server.rulingia.com (8.14.5/8.14.5) with ESMTP id q6N1Np6m009692 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=OK) for ; Mon, 23 Jul 2012 11:23:52 +1000 (EST) (envelope-from stephen@missouri.edu) Received: from wilberforce.math.missouri.edu (wilberforce.math.missouri.edu [128.206.184.213]) by vps.rulingia.com (8.14.5/8.14.5) with ESMTP id q6N1Nnx8010439 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Mon, 23 Jul 2012 11:23:51 +1000 (EST) (envelope-from stephen@missouri.edu) Received: from [127.0.0.1] (wilberforce.math.missouri.edu [128.206.184.213]) by wilberforce.math.missouri.edu (8.14.5/8.14.5) with ESMTP id q6N1NPo6094254; Sun, 22 Jul 2012 20:23:27 -0500 (CDT) (envelope-from stephen@missouri.edu) Message-ID: <500CA78E.2070302@missouri.edu> From: Stephen Montgomery-Smith Mail-Followup-To: freebsd-numerics@freebsd.org User-Agent: Mozilla/5.0 (X11; Linux i686; rv:14.0) Gecko/20120714 Thunderbird/14.0 MIME-Version: 1.0 To: Peter Jeremy References: <20120721032448.X5744@besplex.bde.org> <5009BD6C.9050301@missouri.edu> <20120721123522.T877@besplex.bde.org> <500A2565.9090009@missouri.edu> <20120721181204.A1702@besplex.bde.org> <500B594D.1020305@missouri.edu> <20120722125300.P2246@besplex.bde.org> <500C1B1A.5070107@missouri.edu> <20120723015912.K5029@besplex.bde.org> <500C79A1.6080809@missouri.edu> <20120722231300.GA8033@server.rulingia.com> In-Reply-To: <20120722231300.GA8033@server.rulingia.com> Content-Type: multipart/mixed; boundary="------------030507040607030000090202" X-Content-Filtered-By: Mailman/MimeDel 2.1.5 Cc: Diane Bruce , Bruce Evans , John Baldwin , David Chisnall , Bruce Evans , Steve Kargl , David Schultz , Warner Losh Subject: Re: Use of C99 extra long double math functions after r236148 X-BeenThere: freebsd-numerics@freebsd.org X-Mailman-Version: 2.1.5 Precedence: list List-Id: "Discussions of high quality implementation of libm functions." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Date: Sun, 12 Aug 2012 23:12:38 -0000 X-Original-Date: Sun, 22 Jul 2012 20:23:26 -0500 X-List-Received-Date: Sun, 12 Aug 2012 23:12:38 -0000 This is a multi-part message in MIME format. --------------030507040607030000090202 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit This is what I came up with for catanh. I seem to get a ULP less than 3. On 07/22/2012 06:13 PM, Peter Jeremy wrote: > The "normal" cases are (algorithmetically with '^' as exponentiation): > > catanh(z) = clog((1+z)/(1-z))/2 > = (clog(1+z) - clog(1-z))/2 > catanh(x+I*y) = log((y^2 + (1+x)^2)/(y^2 + (1-x)^2))/4 + I*atan2(y^2, 1-x^2-y^2)/2 > > None of these approaches behave cleanly when |z| is close to 1. If > you have some insights, feel free to work on it. > --------------030507040607030000090202--