From owner-freebsd-numerics@FreeBSD.ORG Wed Dec 3 15:49:46 2014 Return-Path: Delivered-To: freebsd-numerics@freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [8.8.178.115]) (using TLSv1.2 with cipher AECDH-AES256-SHA (256/256 bits)) (No client certificate requested) by hub.freebsd.org (Postfix) with ESMTPS id 636DA5DD for ; Wed, 3 Dec 2014 15:49:46 +0000 (UTC) Received: from troutmask.apl.washington.edu (troutmask.apl.washington.edu [128.95.76.21]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (Client CN "troutmask", Issuer "troutmask" (not verified)) by mx1.freebsd.org (Postfix) with ESMTPS id 40D96C31 for ; Wed, 3 Dec 2014 15:49:46 +0000 (UTC) Received: from troutmask.apl.washington.edu (localhost [127.0.0.1]) by troutmask.apl.washington.edu (8.14.9/8.14.9) with ESMTP id sB3FnidJ001986 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO); Wed, 3 Dec 2014 07:49:44 -0800 (PST) (envelope-from sgk@troutmask.apl.washington.edu) Received: (from sgk@localhost) by troutmask.apl.washington.edu (8.14.9/8.14.9/Submit) id sB3FniT4001985; Wed, 3 Dec 2014 07:49:44 -0800 (PST) (envelope-from sgk) Date: Wed, 3 Dec 2014 07:49:44 -0800 From: Steve Kargl To: Bruce Evans Subject: Re: bug in j0f() Message-ID: <20141203154944.GA1976@troutmask.apl.washington.edu> References: <20141202214325.GA94909@troutmask.apl.washington.edu> <20141203000941.GA98467@troutmask.apl.washington.edu> <20141203002908.GA98589@troutmask.apl.washington.edu> <20141203023207.GA99054@troutmask.apl.washington.edu> <20141203233540.Q44095@besplex.bde.org> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <20141203233540.Q44095@besplex.bde.org> User-Agent: Mutt/1.5.23 (2014-03-12) Cc: freebsd-numerics@freebsd.org X-BeenThere: freebsd-numerics@freebsd.org X-Mailman-Version: 2.1.18-1 Precedence: list List-Id: "Discussions of high quality implementation of libm functions." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 03 Dec 2014 15:49:46 -0000 On Thu, Dec 04, 2014 at 12:08:19AM +1100, Bruce Evans wrote: > On Tue, 2 Dec 2014, Steve Kargl wrote: > > > On Tue, Dec 02, 2014 at 04:29:08PM -0800, Steve Kargl wrote: > >> On Tue, Dec 02, 2014 at 04:09:41PM -0800, Steve Kargl wrote: > >>> On Tue, Dec 02, 2014 at 01:43:25PM -0800, Steve Kargl wrote: > >>>> Anyone object to the following patch? > > OK (with 0x54000000). > > >>>> Index: e_j0f.c > >>>> =================================================================== > >>>> --- e_j0f.c (revision 275211) > >>>> +++ e_j0f.c (working copy) > >>>> @@ -62,7 +62,7 @@ > >>>> * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) > >>>> * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) > >>>> */ > >>>> - if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x); > >>>> + if(ix>0x4b800000) z = (invsqrtpi*cc)/sqrtf(x); > >>> > >>> Exhaustive testing in the range 0x1p38 to 0x1p100 > >>> indicated at the constant should be 0x54000000. > > My tests agree. Tested on amd64 and i386. > > >> Note, a similar wrong condition exists within y0f(). I have > >> not tested y0f(), but propose making a similar change in y0f() > >> as well. > > Not so exhaustive testing gave 0x54800000 on amd64. > Thanks for confirming the values and suggestion the above for y0f(). > > While I'm monologuing, I might as well point out that the > > rational approximations in j0f (and y0f and most likely > > j1f and y1f) are over-specified. I suspect that the > > polynomials in the rational approximation can be reduced > > by one or two terms. > > Also, the cutoffs of 2**-13 and 2**-27 are the same for both precisions, > thus likely to be wrong for float precision. > I haven't gotten that far into analyzing the code. I'll probably get there in a few months. :-) -- Steve