From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 19602 invoked by alias); 6 Jul 2007 17:29:06 -0000 Received: (qmail 19588 invoked by uid 22791); 6 Jul 2007 17:29:06 -0000 X-Spam-Check-By: sourceware.org Received: from e5.ny.us.ibm.com (HELO e5.ny.us.ibm.com) (32.97.182.145) by sourceware.org (qpsmtpd/0.31) with ESMTP; Fri, 06 Jul 2007 17:29:00 +0000 Received: from d01relay02.pok.ibm.com (d01relay02.pok.ibm.com [9.56.227.234]) by e5.ny.us.ibm.com (8.13.8/8.13.8) with ESMTP id l66HSwaE029616 for ; Fri, 6 Jul 2007 13:28:58 -0400 Received: from d01av03.pok.ibm.com (d01av03.pok.ibm.com [9.56.224.217]) by d01relay02.pok.ibm.com (8.13.8/8.13.8/NCO v8.3) with ESMTP id l66HSwZM363320 for ; Fri, 6 Jul 2007 13:28:58 -0400 Received: from d01av03.pok.ibm.com (loopback [127.0.0.1]) by d01av03.pok.ibm.com (8.12.11.20060308/8.13.3) with ESMTP id l66HSvYN031771 for ; Fri, 6 Jul 2007 13:28:58 -0400 Received: from topology.austin.ibm.com (dyn95340157.austin.ibm.com [9.53.40.157]) by d01av03.pok.ibm.com (8.12.11.20060308/8.12.11) with ESMTP id l66HSvrg031761; Fri, 6 Jul 2007 13:28:57 -0400 Received: by topology.austin.ibm.com (Postfix, from userid 1000) id 2527C3A65E; Fri, 6 Jul 2007 12:28:57 -0500 (CDT) Date: Fri, 06 Jul 2007 17:29:00 -0000 To: Michael Cc: gsl-discuss@sources.redhat.com, help-gsl@gnu.org, gmp-discuss@swox.com, mpfr@loria.fr Subject: Re: Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1? Message-ID: <20070706172856.GA4457@austin.ibm.com> References: MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.5.11 From: linas@austin.ibm.com (Linas Vepstas) 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: 2007-q3/txt/msg00007.txt.bz2 On Wed, Jul 04, 2007 at 07:52:21PM -0400, Michael wrote: > Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1? > > Hi all, > > I am looking for a high/multiple precision hypergeometric function > 2F1(a, b, c, z) implementation. My application needs b and c to be > very large, and it is beyond the range of double precision. ? GSL only goes as far as double precision. If b and c are "beyond the range of double precision", then one can get a good approximation by computing 1F0 instead. This isn't what you need? > More specifically, I hope I will be able to looking into the multiple > precision implementation of the hypergeometric function 2F1(a, b, c, > z) and change the power series > > a0+a1*z+a2*z^2+a3*z^3+... > > into > > a0+a1*z1+a2*z2+a3*z3+... !? It is not hard to write code for this. Its maybe 50 lines of code or so. I spent a (very) short afternoon writing 2F1 for GMP, and then tweaking and tesing it. Its not "rocket science". > The whole evaluation of the hypergeometric function has to be > extremely fast for my application. Heh. And how fast must that be? --linas