From owner-freebsd-bugs@FreeBSD.ORG Sat Jul 28 05:36:43 2012 Return-Path: Delivered-To: freebsd-bugs@FreeBSD.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2001:4f8:fff6::34]) by hub.freebsd.org (Postfix) with ESMTP id B2B2E106566B; Sat, 28 Jul 2012 05:36:43 +0000 (UTC) (envelope-from stephen@missouri.edu) Received: from wilberforce.math.missouri.edu (wilberforce.math.missouri.edu [128.206.184.213]) by mx1.freebsd.org (Postfix) with ESMTP id 8417E8FC08; Sat, 28 Jul 2012 05:36:43 +0000 (UTC) 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 q6S5aaFW039838; Sat, 28 Jul 2012 00:36:37 -0500 (CDT) (envelope-from stephen@missouri.edu) Message-ID: <50137A64.3060002@missouri.edu> Date: Sat, 28 Jul 2012 00:36:36 -0500 From: Stephen Montgomery-Smith User-Agent: Mozilla/5.0 (X11; Linux i686; rv:14.0) Gecko/20120714 Thunderbird/14.0 MIME-Version: 1.0 To: Bruce Evans References: <201207270247.q6R2lkeR021134@wilberforce.math.missouri.edu> <20120727233939.A7820@besplex.bde.org> <5012FF06.4030501@missouri.edu> <20120728120632.M909@besplex.bde.org> In-Reply-To: <20120728120632.M909@besplex.bde.org> Content-Type: multipart/mixed; boundary="------------090903080003030709020200" X-Content-Filtered-By: Mailman/MimeDel 2.1.5 Cc: freebsd-bugs@FreeBSD.org, FreeBSD-gnats-submit@FreeBSD.org, Stephen Montgomery-Smith Subject: Re: bin/170206: complex arcsinh, log, etc. X-BeenThere: freebsd-bugs@freebsd.org X-Mailman-Version: 2.1.5 Precedence: list List-Id: Bug reports List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Sat, 28 Jul 2012 05:36:43 -0000 This is a multi-part message in MIME format. --------------090903080003030709020200 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Yes, everywhere I said "double precision" I meant "doubled precision." I think the papers by Hull et al were perfectly happy with a ULP of around 4. I have been trying to do a little better, but like you I am noticing that log1p isn't that good either. I have tried some other things. I am attaching this example which gets a ULP a little over 2. I simulate high precision arithmetic by expanding everything out into integers. I certainly didn't aim for a speedy program. --------------090903080003030709020200--