From owner-freebsd-numerics@FreeBSD.ORG  Wed Aug 15 22:11:24 2012
Return-Path: <owner-freebsd-numerics@FreeBSD.ORG>
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 89F5A106564A
	for <freebsd-numerics@freebsd.org>;
	Wed, 15 Aug 2012 22:11:24 +0000 (UTC)
	(envelope-from stephen@missouri.edu)
Received: from wilberforce.math.missouri.edu (wilberforce.math.missouri.edu
	[128.206.184.213])
	by mx1.freebsd.org (Postfix) with ESMTP id 487628FC18
	for <freebsd-numerics@freebsd.org>;
	Wed, 15 Aug 2012 22:11:22 +0000 (UTC)
Received: from [127.0.0.1] (wilberforce.math.missouri.edu [128.206.184.213])
	by wilberforce.math.missouri.edu (8.14.5/8.14.5) with ESMTP id
	q7FMBLNF066952 for <freebsd-numerics@freebsd.org>;
	Wed, 15 Aug 2012 17:11:21 -0500 (CDT)
	(envelope-from stephen@missouri.edu)
Message-ID: <502C1E89.9070408@missouri.edu>
Date: Wed, 15 Aug 2012 17:11:21 -0500
From: Stephen Montgomery-Smith <stephen@missouri.edu>
User-Agent: Mozilla/5.0 (X11; Linux i686;
	rv:14.0) Gecko/20120714 Thunderbird/14.0
MIME-Version: 1.0
To: freebsd-numerics@freebsd.org
References: <5017111E.6060003@missouri.edu> <501C361D.4010807@missouri.edu>
	<20120804165555.X1231@besplex.bde.org>
	<501D51D7.1020101@missouri.edu>
	<20120805030609.R3101@besplex.bde.org>
	<501D9C36.2040207@missouri.edu>
	<20120805175106.X3574@besplex.bde.org>
	<501EC015.3000808@missouri.edu>
	<20120805191954.GA50379@troutmask.apl.washington.edu>
	<20120807205725.GA10572@server.rulingia.com>
	<20120809025220.N4114@besplex.bde.org>
	<5027F07E.9060409@missouri.edu>
	<20120814003614.H3692@besplex.bde.org>
	<50295F5C.6010800@missouri.edu>
	<20120814072946.S5260@besplex.bde.org>
	<50297CA5.5010900@missouri.edu> <50297E43.7090309@missouri.edu>
	<20120814201105.T934@besplex.bde.org>
	<502C0998.7040004@missouri.edu> <502C194D.50903@missouri.edu>
In-Reply-To: <502C194D.50903@missouri.edu>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Subject: Re: Complex arg-trig functions
X-BeenThere: freebsd-numerics@freebsd.org
X-Mailman-Version: 2.1.5
Precedence: list
List-Id: "Discussions of high quality implementation of libm functions."
	<freebsd-numerics.freebsd.org>
List-Unsubscribe: <http://lists.freebsd.org/mailman/listinfo/freebsd-numerics>, 
	<mailto:freebsd-numerics-request@freebsd.org?subject=unsubscribe>
List-Archive: <http://lists.freebsd.org/pipermail/freebsd-numerics>
List-Post: <mailto:freebsd-numerics@freebsd.org>
List-Help: <mailto:freebsd-numerics-request@freebsd.org?subject=help>
List-Subscribe: <http://lists.freebsd.org/mailman/listinfo/freebsd-numerics>, 
	<mailto:freebsd-numerics-request@freebsd.org?subject=subscribe>
X-List-Received-Date: Wed, 15 Aug 2012 22:11:24 -0000

On 08/15/2012 04:49 PM, Stephen Montgomery-Smith wrote:
> On 08/15/2012 03:42 PM, Stephen Montgomery-Smith wrote:
>
>>
>> All your solutions depend upon using (1-tiny) with the result being
>> used.  But what if FE_DOWNWARD is set?  Then 1-tiny becomes
>> 1-DBL_EPSILON.  And then if the result is used, everything is off by 1
>> ulp.
>>
>> And
>> if ((int)(1 - tiny) == 1)
>> will fail.
>
> How about replacing
>
>      if (huge+ax>one && huge+bx>one) ....
>
> with
>
>      if ((int)(1/ax)==0 || (int)(1/bx)==0) ....
>
> (We know that one of ax or bx is larger than 1.)

if ((int)(1/(2+ax))==0) ....

(because one of ax or bx might be 0).