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 SAA13598; Wed, 28 Mar 2001 18:14:00 +0200 (MET DST) X-Authentication-Warning: pauillac.inria.fr: majordomo set sender to owner-caml-list@pauillac.inria.fr using -f Received: from nez-perce.inria.fr (nez-perce.inria.fr [192.93.2.78]) by pauillac.inria.fr (8.7.6/8.7.3) with ESMTP id SAA13593 for ; Wed, 28 Mar 2001 18:13:59 +0200 (MET DST) Received: from blount.mail.mindspring.net (blount.mail.mindspring.net [207.69.200.226]) by nez-perce.inria.fr (8.11.1/8.10.0) with ESMTP id f2SGDvP01952 for ; Wed, 28 Mar 2001 18:13:58 +0200 (MET DST) Received: from dylan (1Cust209.tnt3.tucson.az.da.uu.net [63.11.144.209]) by blount.mail.mindspring.net (8.9.3/8.8.5) with SMTP id LAA22906 for ; Wed, 28 Mar 2001 11:13:47 -0500 (EST) Message-ID: <000901c0b7a2$20e18750$210148bf@dylan> From: "David McClain" To: Subject: [Caml-list] Complex Arithmetic Date: Wed, 28 Mar 2001 09:14:08 -0700 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2919.6600 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2919.6600 Sender: owner-caml-list@pauillac.inria.fr Precedence: bulk Hi! I want to thank all of you on this topic for helping point out the wider meaning of Kahan's statement. After getting some sleep I now realize the "Eureka!" that I missed in the wider sense, along with every other language (that I know about) that uses rectangular mapping of the complex plane. I need to stop working all night into the red-eye zone so that these things become a bit more apparent on first glimpse... Indeed a rectangular representation *IS* insufficient and something which also encodes the Riemann sheet is needed to properly handle all possibilities. Will I fix NML in this regard? Probably not... simply because letter-perfect complex arithmetic is so rarely needed in practice. But I might play around with a limited class of compelx numbers that do things correctly. I wouldn't want to hose down the performance of my FFT's and such. - DM ------------------- To unsubscribe, mail caml-list-request@inria.fr. Archives: http://caml.inria.fr