From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 10947 invoked by alias); 17 Mar 2009 16:23:09 -0000 Received: (qmail 10877 invoked by uid 22791); 17 Mar 2009 16:23:07 -0000 X-SWARE-Spam-Status: No, hits=-1.7 required=5.0 tests=AWL,BAYES_00,J_CHICKENPOX_64 X-Spam-Check-By: sourceware.org Received: from qmta03.emeryville.ca.mail.comcast.net (HELO QMTA03.emeryville.ca.mail.comcast.net) (76.96.30.32) by sourceware.org (qpsmtpd/0.43rc1) with ESMTP; Tue, 17 Mar 2009 16:23:02 +0000 Received: from OMTA07.emeryville.ca.mail.comcast.net ([76.96.30.59]) by QMTA03.emeryville.ca.mail.comcast.net with comcast id UFhp1b0091GXsucA3GP1wN; Tue, 17 Mar 2009 16:23:01 +0000 Received: from hippogriff.homeunix.org ([24.8.141.236]) by OMTA07.emeryville.ca.mail.comcast.net with comcast id UGP11b00A56DT748TGP1PK; Tue, 17 Mar 2009 16:23:01 +0000 Received: by hippogriff.homeunix.org (Postfix, from userid 1000) id AB4C6CB3F0; Tue, 17 Mar 2009 10:25:36 -0600 (MDT) Date: Tue, 17 Mar 2009 16:23:00 -0000 From: Patrick Alken To: gsl-discuss@sourceware.org Subject: Re: New extension for Associated Legendre Functions (ALFs) Message-ID: <20090317162536.GA22060@hippogriff.homeunix.org> References: <20090316213137.GA4277@hippogriff.homeunix.org> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.5.18 (2008-05-17) Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org X-SW-Source: 2009-q1/txt/msg00022.txt.bz2 I should also mention that I played around with computing ALFs using quad precision in the recurrence relations. In doing this you can avoid underflow problems to degrees up in the 10s of thousands (I only tried up to L,M = 20000). But unfortunately I don't think sizeof(long double) is standard, though I do think its guaranteed to be at least 10 bytes by the latest ansi standard. So for now I left everything in double precision. Patrick On Tue, Mar 17, 2009 at 11:28:52AM +0000, Brian Gough wrote: > At Mon, 16 Mar 2009 15:31:37 -0600, > Patrick Alken wrote: > > Most current implementations of associated Legendre functions > > (ALFs), including the current GSL version fail due to underflow > > above degree and order (L,M) 1900. A 2002 paper by Holmes and > > Featherstone shows that with a very simple scaling modification > > this limit can be extended to 2700 in double precision. I have > > recently needed to compute high degree ALFs so I have implemented > > their algorithm and made a new GSL extension if others are interested. > > Great work! > > Incidentally, I found a copy of their paper online at > http://www.cage.curtin.edu.au/~geogrp/research.html > http://www.cage.curtin.edu.au/~will/20760279.pdf > > -- > Brian Gough