From owner-freebsd-numerics@FreeBSD.ORG Sun Aug 12 23:08:42 2012 Return-Path: Delivered-To: freebsd-numerics@freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [69.147.83.52]) by hub.freebsd.org (Postfix) with ESMTP id 815B51065672 for ; Sun, 12 Aug 2012 23:08:42 +0000 (UTC) (envelope-from peter@rulingia.com) Received: from vps.rulingia.com (host-122-100-2-194.octopus.com.au [122.100.2.194]) by mx1.freebsd.org (Postfix) with ESMTP id 1A7208FC0C for ; Sun, 12 Aug 2012 23:08:41 +0000 (UTC) Received: from server.rulingia.com (c220-239-249-137.belrs5.nsw.optusnet.com.au [220.239.249.137]) by vps.rulingia.com (8.14.5/8.14.5) with ESMTP id q7CN8fF0075750 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=OK) for ; Mon, 13 Aug 2012 09:08:42 +1000 (EST) (envelope-from peter@rulingia.com) X-Bogosity: Ham, spamicity=0.000000 Received: from server.rulingia.com (localhost.rulingia.com [127.0.0.1]) by server.rulingia.com (8.14.5/8.14.5) with ESMTP id q7CN8Zp7021460 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Mon, 13 Aug 2012 09:08:35 +1000 (EST) (envelope-from peter@server.rulingia.com) Received: (from peter@localhost) by server.rulingia.com (8.14.5/8.14.5/Submit) id q7CN8ZIL021459 for freebsd-numerics@freebsd.org; Mon, 13 Aug 2012 09:08:35 +1000 (EST) (envelope-from peter) Resent-From: Peter Jeremy Resent-Date: Mon, 13 Aug 2012 09:08:35 +1000 Resent-Message-ID: <20120812230835.GG20453@server.rulingia.com> Resent-To: freebsd-numerics@freebsd.org Received: from vps.rulingia.com (host-122-100-2-194.octopus.com.au [122.100.2.194]) by server.rulingia.com (8.14.5/8.14.5) with ESMTP id q6J2ro0A008593 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=OK) for ; Thu, 19 Jul 2012 12:53:51 +1000 (EST) (envelope-from sgk@troutmask.apl.washington.edu) Received: from troutmask.apl.washington.edu (troutmask.apl.washington.edu [128.95.76.21]) by vps.rulingia.com (8.14.5/8.14.5) with ESMTP id q6J2rmqD079030 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Thu, 19 Jul 2012 12:53:50 +1000 (EST) (envelope-from sgk@troutmask.apl.washington.edu) Received: from troutmask.apl.washington.edu (localhost.apl.washington.edu [127.0.0.1]) by troutmask.apl.washington.edu (8.14.5/8.14.5) with ESMTP id q6J2rkYq001416; Wed, 18 Jul 2012 19:53:46 -0700 (PDT) (envelope-from sgk@troutmask.apl.washington.edu) Received: (from sgk@localhost) by troutmask.apl.washington.edu (8.14.5/8.14.5/Submit) id q6J2rjga001415; Wed, 18 Jul 2012 19:53:45 -0700 (PDT) (envelope-from sgk) From: Steve Kargl Mail-Followup-To: freebsd-numerics@freebsd.org To: Stephen Montgomery-Smith Message-ID: <20120719025345.GA1376@troutmask.apl.washington.edu> References: <20120713155805.GC81965@zim.MIT.EDU> <20120714120432.GA70706@server.rulingia.com> <20120717084457.U3890@besplex.bde.org> <5004A5C7.1040405@missouri.edu> <5004DEA9.1050001@missouri.edu> <20120717200931.U6624@besplex.bde.org> <5006D13D.2080702@missouri.edu> <20120718205625.GA409@troutmask.apl.washington.edu> <500725F2.7060603@missouri.edu> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <500725F2.7060603@missouri.edu> User-Agent: Mutt/1.4.2.3i Cc: Diane Bruce , John Baldwin , David Chisnall , Bruce Evans , Bruce Evans , David Schultz , Peter Jeremy , Warner Losh Subject: Re: Use of C99 extra long double math functions after r236148 X-BeenThere: freebsd-numerics@freebsd.org X-Mailman-Version: 2.1.5 Precedence: list List-Id: "Discussions of high quality implementation of libm functions." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Date: Sun, 12 Aug 2012 23:08:42 -0000 X-Original-Date: Wed, 18 Jul 2012 19:53:45 -0700 X-List-Received-Date: Sun, 12 Aug 2012 23:08:42 -0000 On Wed, Jul 18, 2012 at 04:09:06PM -0500, Stephen Montgomery-Smith wrote: > On 07/18/2012 03:56 PM, Steve Kargl wrote: > >On Wed, Jul 18, 2012 at 10:07:41AM -0500, Stephen Montgomery-Smith wrote: > >> > >>>The most obvious immediate difficulty in translating the above into C is > >>>that y*y and z*z may overflow when the result shouldn't. > >> > >>This will be a lot easier than I originally expected. When we are in > >>conditions when overflow might occur, we can simply make the > >>approximations > >>sqrt(y*y-1) = y > >>csqrt(z*z+1) = signum(x)*z > >>because in floating point arithmetic, these will not be approximations, > >>but true exactly. And I am thinking that the test I will use for when > >>to use these approximations will be (y==y+1) and (z==z+1) respectively. > >> (I would use (z*z==z*z+1) but that test has the overflow problem.) > > > >I could be mistaken, but I believe that you need to raise the > >inexact flag with these approximations because in fact you > >are doing floating point math. > > > > Thanks for this observation. I am looking through the C99 standard, > trying to understand the inexact flag. But I am struggling to interpret it. > > Am I to understand that the inexact flag should be set anytime a > floating point operation produces an answer that is not guaranteed > exact? For example, should 1.0/3.0 and sqrt(2.0) raise the inexact flag? The inexact flag will get raised by the fpu, but you need to cause the condition. For your 'sqrt(y*y-1) = y' example, you would do something like 'sqrt(y*y-1) = abs(y) - tiny' where tiny is much less than abs(y). Search msun/src for inexact (ie., grep -i inexact msun/src/*.c) -- Steve