From owner-freebsd-numerics@FreeBSD.ORG Sun Aug 12 23:12:46 2012 Return-Path: Delivered-To: freebsd-numerics@freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2001:4f8:fff6::34]) by hub.freebsd.org (Postfix) with ESMTP id 673C51065673 for ; Sun, 12 Aug 2012 23:12:46 +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 C603A8FC12 for ; Sun, 12 Aug 2012 23:12:45 +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 q7CNCjHW075926 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=OK) for ; Mon, 13 Aug 2012 09:12:45 +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 q7CNCdaL021828 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Mon, 13 Aug 2012 09:12:39 +1000 (EST) (envelope-from peter@server.rulingia.com) Received: (from peter@localhost) by server.rulingia.com (8.14.5/8.14.5/Submit) id q7CNCdfH021827 for freebsd-numerics@freebsd.org; Mon, 13 Aug 2012 09:12:39 +1000 (EST) (envelope-from peter) Resent-From: Peter Jeremy Resent-Date: Mon, 13 Aug 2012 09:12:39 +1000 Resent-Message-ID: <20120812231239.GU20453@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 q6MFgWNg097070 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=OK) for ; Mon, 23 Jul 2012 01:42:32 +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 q6MFgTwE006732 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Mon, 23 Jul 2012 01:42:31 +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 q6MFg8dJ055307; Sun, 22 Jul 2012 10:42:08 -0500 (CDT) (envelope-from stephen@missouri.edu) Message-ID: <500C1F51.7050209@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: Bruce Evans References: <20120714120432.GA70706@server.rulingia.com> <5004A5C7.1040405@missouri.edu> <5004DEA9.1050001@missouri.edu> <20120717200931.U6624@besplex.bde.org> <5006D13D.2080702@missouri.edu> <20120718205625.GA409@troutmask.apl.washington.edu> <500725F2.7060603@missouri.edu> <20120719025345.GA1376@troutmask.apl.washington.edu> <50077987.1080307@missouri.edu> <20120719032706.GA1558@troutmask.apl.washington.edu> <5007826D.7060806@missouri.edu> <5007AD41.9070000@missouri.edu> <20120719205347.T2601@besplex.bde.org> <50084322.7020401@missouri.edu> <20120720035001.W4053@besplex.bde.org> <50085441.4090305@missouri.edu> <20120720162953.N2162@besplex.bde.org> <20120720184114.B2790@besplex.bde.org> <50097128.6030405@missouri.edu> <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> In-Reply-To: <20120722125300.P2246@besplex.bde.org> Content-Type: multipart/mixed; boundary="------------040203020507050000080401" X-Content-Filtered-By: Mailman/MimeDel 2.1.5 Cc: Diane Bruce , John Baldwin , David Chisnall , Bruce Evans , Steve Kargl , David Schultz , Peter Jeremy , 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 23:12:46 -0000 X-Original-Date: Sun, 22 Jul 2012 10:42:09 -0500 X-List-Received-Date: Sun, 12 Aug 2012 23:12:46 -0000 This is a multi-part message in MIME format. --------------040203020507050000080401 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit On 07/22/2012 01:19 AM, Bruce Evans wrote: >> 2. I have thought more about the problem of computing clog(z) when >> |z| is close to 1. I now think it might even require precision that >> is 3 times better than double precision. >> It is possible that you could, by chance, pick x and y so that |z| = 1 >> + 1e30. (I wrote a test program, and this did > e-30 here and elsewhere >> actually happen a few times.) So when you compute x^2+y^2-1, if you >> do it using double double precision, you will get 2e30, but only the >> most significant digits will be accurate. The ULP will be about >> 1e15. You need triple double precision to get ULP's close to 1. > > Hmm, I'm not seeing such cases except when |x| or |y| is 1 and the other > is tiny. That was my mistake. I didn't have enough precision in mpfr to use it as a proper reference! Now I tested my code, and I seem to be getting ULP's consistently less than 2! I am attaching my clog code and my test code. I go in and manually change the test code to test around a different range of values. --------------040203020507050000080401--