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 FAA11050; Sat, 6 Dec 2003 05:42:48 +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 FAA11214 for ; Sat, 6 Dec 2003 05:42:46 +0100 (MET) Received: from mail3.tpgi.com.au (mail.tpgi.com.au [203.12.160.59]) by concorde.inria.fr (8.11.1/8.11.1) with ESMTP id hB64gir00805 for ; Sat, 6 Dec 2003 05:42:45 +0100 (MET) Received: from syd-ts22-2600-164.tpgi.com.au (syd-ts22-2600-164.tpgi.com.au [203.26.30.164]) by mail3.tpgi.com.au (8.11.6/8.11.6) with ESMTP id hB64gf501298 for ; Sat, 6 Dec 2003 15:42:41 +1100 Subject: Re: [Caml-list] float type with better precision than the default From: skaller Reply-To: skaller@ozemail.com.au To: Ocaml Mailing List In-Reply-To: References: Content-Type: text/plain Message-Id: <1070682167.6259.31.camel@pelican> Mime-Version: 1.0 X-Mailer: Ximian Evolution 1.2.2 (1.2.2-4) Date: 06 Dec 2003 14:42:50 +1100 Content-Transfer-Encoding: 7bit X-Loop: caml-list@inria.fr X-Spam: no; 0.00; caml-list:01 ozemail:01 scalar:01 vectors:01 quantum:99 float:02 wrote:03 decimal:05 brian:06 product:92 type:07 problem:07 problem:07 standard:07 consider:09 Sender: owner-caml-list@pauillac.inria.fr Precedence: bulk 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) and you can see you need around 50 digits precision, just to get an answer with 1 digit of precision. The eigen problem with large numbers of dimensions arises in, for example, quantum chemistry. ------------------- 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