From mboxrd@z Thu Jan 1 00:00:00 1970 Received: (from majordomo@localhost) by pauillac.inria.fr (8.7.6/8.7.3) id MAA22383; Sat, 6 Dec 2003 12:54:44 +0100 (MET) X-Authentication-Warning: pauillac.inria.fr: majordomo set sender to owner-caml-list@pauillac.inria.fr using -f Received: from concorde.inria.fr (concorde.inria.fr [192.93.2.39]) by pauillac.inria.fr (8.7.6/8.7.3) with ESMTP id MAA21643 for ; Sat, 6 Dec 2003 12:54:43 +0100 (MET) Received: from mwinf0302.wanadoo.fr (smtp3.wanadoo.fr [193.252.22.28]) by concorde.inria.fr (8.11.1/8.11.1) with ESMTP id hB6Bsgr27960 for ; Sat, 6 Dec 2003 12:54:42 +0100 (MET) Received: from debian (ca-bordeaux-4-47.w80-8.abo.wanadoo.fr [80.8.76.47]) by mwinf0302.wanadoo.fr (SMTP Server) with ESMTP id 5BFBBC00025F for ; Sat, 6 Dec 2003 12:54:42 +0100 (CET) Received: from moi by debian with local (Exim 3.36 #1 (Debian)) id 1ASb1M-0000sz-00 for ; Sat, 06 Dec 2003 12:54:48 +0100 To: caml-list@inria.fr Subject: Re: [Caml-list] float type with better precision than the default References: <1070682167.6259.31.camel@pelican> From: Remi Vanicat Mail-Copy-To: never Date: Sat, 06 Dec 2003 12:54:47 +0100 In-Reply-To: <1070682167.6259.31.camel@pelican> (skaller@ozemail.com.au's message of "06 Dec 2003 14:42:50 +1100") Message-ID: <87k75axit4.dlv@wanadoo.fr> User-Agent: Gnus/5.1003 (Gnus v5.10.3) Emacs/21.3 (gnu/linux) MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-15 Content-Transfer-Encoding: 8bit X-Loop: caml-list@inria.fr X-Spam: no; 0.00; caml-list:01 ozemail:01 scalar:01 vectors:01 writes:01 remi:01 remi:01 vanicat:01 vanicat:01 float:02 wrote:03 algorithm:03 decimal:05 numerical:05 brian:06 Sender: owner-caml-list@pauillac.inria.fr Precedence: bulk skaller writes: > On Sat, 2003-12-06 at 14:18, Brian Hurt wrote: >> 30 decimal digits is enough accuracy to measure the >> distance between here and the Andromeda Galaxy in microns. Why does he >> need such a ridiculous amount of precision? > > Standard eigen problem sometimes needs ridiculous precision: > the scalar product of two vectors: > > sigma (i=1,n) (v1_i * v2_i) > > sometimes involves cancellation of large values. > To see why there is a problem here, consider: > > 1.000001e20 - 1e20 - > (1.000001e-20 - 1e-20) > [...] This is what is called a numerical unstable algorithm... -- Rémi Vanicat ------------------- To unsubscribe, mail caml-list-request@inria.fr Archives: http://caml.inria.fr Bug reports: http://caml.inria.fr/bin/caml-bugs FAQ: http://caml.inria.fr/FAQ/ Beginner's list: http://groups.yahoo.com/group/ocaml_beginners