From malcolm@brackley.nag.co.uk Wed Jan 24 14:56:06 2001 Received: from server-5.tower-4.starlabs.net (mail.london-1.starlabs.net [212.125.75.12]) by dkuug.dk (8.9.2/8.9.2) with SMTP id OAA16900 for ; Wed, 24 Jan 2001 14:56:02 +0100 (CET) (envelope-from malcolm@brackley.nag.co.uk) X-VirusChecked: Checked Received: (qmail 24659 invoked from network); 24 Jan 2001 13:55:09 -0000 Received: from nagmx1e.nag.co.uk (HELO nag.co.uk) (62.232.54.130) by server-5.tower-4.starlabs.net with SMTP; 24 Jan 2001 13:55:09 -0000 Received: from brackley.nag.co.uk (brackley.nag.co.uk [192.156.217.21]) by nag.co.uk (8.9.3/8.9.3) with ESMTP id NAA03869 for ; Wed, 24 Jan 2001 13:55:43 GMT Received: (from malcolm@localhost) by brackley.nag.co.uk (8.9.3/8.9.3) id NAA58686 for sc22wg5@dkuug.dk; Wed, 24 Jan 2001 13:57:54 GMT (envelope-from malcolm) From: Malcolm Cohen Message-Id: <200101241357.NAA58686@brackley.nag.co.uk> Subject: Re: (SC22WG5.1991) N1423: WG5 letter ballot on interpretations To: sc22wg5@dkuug.dk Date: Wed, 24 Jan 2001 13:57:54 +0000 (GMT) X-Mailer: ELM [version 2.4ME+ PL61 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit D Muxworthy asked: > it would > be helpful to have a note in F200x highlighting this difference, and > giving an example of when NEAREST(X,1.) is different from X + > SPACING(X). Is this likely to be true only at extreme values? Not in general (though for "normal" floating point types, yes). Consider double precision implemented as double+double (the second double being at least 2**53 smaller than the first double). The Brown model for this will have 106 bits, so SPACING(1.0) will be approximately 2**(-106). However, if X is *exactly* 1.0, then NEAREST(X,1.) will be 1.0 plus the smallest representable double, i.e. approx 1+10**(-308). The Brown model has lots of other problems with double+double, not just this one; basically the model is too simplistic. So the other "model number" intrinsics (TINY, HUGE, MAXEXPONENT, et al) also have slight anomalies for this data type. Cheers, -- ...........................Malcolm Cohen, NAG Ltd., Oxford, U.K. (malcolm@nag.co.uk) _____________________________________________________________________ This message has been checked for all known viruses by Star Internet delivered through the MessageLabs Virus Control Centre. For further information visit http://www.star.net.uk/stats.asp