From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 1571 invoked by alias); 22 Jun 2009 14:00:44 -0000 Received: (qmail 1562 invoked by uid 22791); 22 Jun 2009 14:00:42 -0000 X-SWARE-Spam-Status: No, hits=-1.6 required=5.0 tests=AWL,BAYES_00,SARE_MSGID_LONG40,SPF_PASS X-Spam-Check-By: sourceware.org Received: from mail-ew0-f228.google.com (HELO mail-ew0-f228.google.com) (209.85.219.228) by sourceware.org (qpsmtpd/0.43rc1) with ESMTP; Mon, 22 Jun 2009 14:00:37 +0000 Received: by ewy28 with SMTP id 28so4774604ewy.24 for ; Mon, 22 Jun 2009 07:00:34 -0700 (PDT) MIME-Version: 1.0 Received: by 10.216.1.69 with SMTP id 47mr2244166wec.224.1245679232120; Mon, 22 Jun 2009 07:00:32 -0700 (PDT) In-Reply-To: <4a00655d0906211331y127e5693uda4805cf347561b3@mail.gmail.com> References: <4a00655d0906211327x742b7224of110fa0621fbbad9@mail.gmail.com> <4a00655d0906211331y127e5693uda4805cf347561b3@mail.gmail.com> From: Rhys Ulerich Date: Mon, 22 Jun 2009 14:00:00 -0000 Message-ID: <4a00655d0906220700o4422e01s46edd50c8c4a1f95@mail.gmail.com> Subject: Re: [PATCH] Adding fixed-order Gauss-Legendre integration routines To: gsl-discuss@sourceware.org Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit 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-q2/txt/msg00028.txt.bz2 > The routines include precomputed full double precision points and > weights for n = 2, ..., 512, and 1024 Gauss points. If the user selects > any other number, the necessary points and weights are computed > on the fly and remain quite good. A quick comment from Pavel about the numerical precision in the patch's coefficients... > ... fixed tables included in [the patch] are way beyond full double precision. > Full double precision is about 1e-16, fixed tables are of 1e-25. > This doesn't hurt the double calculations and allows future extensions > e.g. for 'long double' and multi-precision libraries (like gmp or mpfr). > > Tables generated on the fly are of 1e-10, which is pretty much the > maximum precision we can get using double to calculate weights. > So, on-the-fly tables are of full double precision, fixed have much > higher precision. - Rhys