From owner-freebsd-numerics@FreeBSD.ORG Wed Dec 3 13:08:30 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 1DBEB712 for ; Wed, 3 Dec 2014 13:08:30 +0000 (UTC) Received: from mail104.syd.optusnet.com.au (mail104.syd.optusnet.com.au [211.29.132.246]) by mx1.freebsd.org (Postfix) with ESMTP id D3C402DE for ; Wed, 3 Dec 2014 13:08:29 +0000 (UTC) Received: from c122-106-147-133.carlnfd1.nsw.optusnet.com.au (c122-106-147-133.carlnfd1.nsw.optusnet.com.au [122.106.147.133]) by mail104.syd.optusnet.com.au (Postfix) with ESMTPS id 2429E42555E; Thu, 4 Dec 2014 00:08:19 +1100 (AEDT) Date: Thu, 4 Dec 2014 00:08:19 +1100 (EST) From: Bruce Evans X-X-Sender: bde@besplex.bde.org To: Steve Kargl Subject: Re: bug in j0f() In-Reply-To: <20141203023207.GA99054@troutmask.apl.washington.edu> Message-ID: <20141203233540.Q44095@besplex.bde.org> 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> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Optus-CM-Score: 0 X-Optus-CM-Analysis: v=2.1 cv=dMCfxopb c=1 sm=1 tr=0 a=7NqvjVvQucbO2RlWB8PEog==:117 a=PO7r1zJSAAAA:8 a=kj9zAlcOel0A:10 a=JzwRw_2MAAAA:8 a=cVtEa_Lb80mRl8RVK4oA:9 a=CjuIK1q_8ugA:10 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 13:08:30 -0000 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. > 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. Bruce