From owner-sc22wg5@open-std.org Sat Oct 8 16:53:52 2005 Return-Path: X-Original-To: sc22wg5-domo2 Delivered-To: sc22wg5-domo2@open-std.org Received: by open-std.org (Postfix, from userid 521) id 04D56152BC; Sat, 8 Oct 2005 16:53:51 +0200 (CET DST) X-Original-To: sc22wg5@open-std.org Delivered-To: sc22wg5@open-std.org Received: from dkuug.dk (ptah.dkuug.dk [195.215.30.66]) by open-std.org (Postfix) with ESMTP id 0D518113B6 for ; Sat, 8 Oct 2005 16:53:49 +0200 (CET DST) Received: from mx3.liv.ac.uk (mx3.liv.ac.uk [138.253.100.181]) by dkuug.dk (8.12.10/8.9.2) with ESMTP id j98EqqbU026504 for ; Sat, 8 Oct 2005 16:52:58 +0200 (CEST) (envelope-from j.l.schonfelder@liverpool.ac.uk) Received: from mailhub1.liv.ac.uk ([138.253.100.94]) by mx3.liv.ac.uk with esmtp (Exim 4.52) id 1EOFN6-0004EZ-EH for sc22wg5@dkuug.dk; Sat, 08 Oct 2005 15:08:20 +0100 Received: from localhost ([127.0.0.1] helo=mailhub1.liv.ac.uk) by mailhub1.liv.ac.uk with esmtp (Exim 4.52) id 1EOFN6-0006Ib-BJ for sc22wg5@dkuug.dk; Sat, 08 Oct 2005 15:08:20 +0100 Received: from host217-42-104-141.range217-42.btcentralplus.com ([217.42.104.141] helo=[192.168.0.2]) by mailhub1.liv.ac.uk with esmtpsa (TLSv1:DES-CBC3-SHA:168) (Exim 4.52) id 1EOFN6-0006IY-5Z for sc22wg5@dkuug.dk; Sat, 08 Oct 2005 15:08:20 +0100 Date: Sat, 08 Oct 2005 15:08:19 +0100 From: "J.L.Schonfelder" To: WG5 Subject: Re: (j3.2005) (SC22WG5.3318) SC22 meeting Message-ID: In-Reply-To: <20051007143249.EA5CB13E6D@open-std.org> References: <20051007143249.EA5CB13E6D@open-std.org> X-Mailer: Mulberry/3.1.6 (Win32) MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Content-Disposition: inline X-Spam-Score: 0 () Sender: owner-sc22wg5@open-std.org Precedence: bulk --On 07 October 2005 15:33 +0100 John Reid wrote: > 1. Resolution 05-08: Revision of IEEE 754 Standard for Floating-Point > Arithmetic > > We are asked to provide our input regarding requirements for our decimal > floating-point work. The Cobol convener gave me to understand that the > current problems are associated with choosing the base: 10 or 1000. Cobol > very firmly wants 10. I said that we had no strong views on this and > would probably support whatever the standard finally says. Does anyone > disagree? > A base 10 arithmetic and a base 1000 are commensurate in that the conversion from one to the other is almost trivial and exact. However there are some significant differences. 1000 is clearly advantageous from an efficiency of implementation point of view. A single base 1000 digit (equiv to 3 decimal digits) can be very efficiently packed into 10 bits (1023). If one then uses a standard fixed precision representation and a normalisation to base 1000 exponent a very straight forward arithmetic results. This unfortunately suffers from the wobbling word length effect common to large base arithmetics, c.f. the well known effect with HEX floating point verses binary in the same wordlength. The problem with base 1000 is of course greatly compounded. For example, with a normalisation with leading digit non-zero (standard practice) it would be possible that only one of the possible three decimal digits representable would be determined and hence a potential 2D loss of precision. Or to put it another way to guarantee 6 decimal digits of accuracy you would need to retain 3 base 1000 digits. This effect would be likely to negate the efficiency gain by using base 1000 in the first place. The probable solution would be to operate with a base 10 normalisation but to use a representation that effectively packed 3D into each 10 bits. I remember Kahan advocating such a system about 30 years ago. My view is that I believe the Cobol people are probably right but whether for the right reason is not clear. I do not think a true base 1000 arithmetic is desirable but a mixed system with base 1000 digit packing but base 10 normalisation is entirely possible and if Kahan was right (he usually was) the complications involved were not so great and they could all be implemented in silicone so as to be hidden from the average user. -- Dr. Lawrie Schonfelder Honorary Senior Fellow, University of Liverpool Home: 1 Marine Park, West Kirby, Wirral, UK, CH48 5HN Phone: +44 (151) 625 6986