From owner-freebsd-current@FreeBSD.ORG Tue Jul 10 16:40:06 2012 Return-Path: Delivered-To: freebsd-current@freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [69.147.83.52]) by hub.freebsd.org (Postfix) with ESMTP id 8D0E2106566B for ; Tue, 10 Jul 2012 16:40:06 +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 4D4DA8FC14 for ; Tue, 10 Jul 2012 16:40:06 +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 q6AGdxnF004284; Tue, 10 Jul 2012 11:39:59 -0500 (CDT) (envelope-from stephen@missouri.edu) Message-ID: <4FFC5ADF.2010601@missouri.edu> Date: Tue, 10 Jul 2012 11:39:59 -0500 From: Stephen Montgomery-Smith User-Agent: Mozilla/5.0 (X11; Linux i686; rv:13.0) Gecko/20120615 Thunderbird/13.0.1 MIME-Version: 1.0 To: Steve Kargl References: <20120529000756.GA77386@troutmask.apl.washington.edu> <4FC43C8F.5090509@missouri.edu> <20120529045612.GB4445@server.rulingia.com> <20120708124047.GA44061@zim.MIT.EDU> <210816F0-7ED7-4481-ABFF-C94A700A3EA0@bsdimp.com> <4FF9DA46.2010502@missouri.edu> <20120708235848.GB53462@troutmask.apl.washington.edu> <4FFA25EA.5090705@missouri.edu> <20120709020107.GA53977@troutmask.apl.washington.edu> <4FFA52F8.2080700@missouri.edu> <20120709050238.GA54634@troutmask.apl.washington.edu> In-Reply-To: <20120709050238.GA54634@troutmask.apl.washington.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Cc: freebsd-current@freebsd.org Subject: Re: Use of C99 extra long double math functions after r236148 X-BeenThere: freebsd-current@freebsd.org X-Mailman-Version: 2.1.5 Precedence: list List-Id: Discussions about the use of FreeBSD-current List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Tue, 10 Jul 2012 16:40:06 -0000 On 07/09/2012 12:02 AM, Steve Kargl wrote: > Yep. Another example is the use of upward recurion to compute > Bessel functions where the argument is larger than the order. > The algorithm is known to be unstable. By upward recursion, do you mean equation (1) in http://mathworld.wolfram.com/BesselFunction.html? So what do people use. Maybe something like http://en.wikipedia.org/wiki/Bessel_function#Asymptotic_forms (second set of equations), but finding some asymptotics with a few extra terms in them?