From owner-freebsd-standards@freebsd.org Mon Apr 24 23:55:39 2017 Return-Path: Delivered-To: freebsd-standards@mailman.ysv.freebsd.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2001:1900:2254:206a::19:1]) by mailman.ysv.freebsd.org (Postfix) with ESMTP id D117ED4EB18; Mon, 24 Apr 2017 23:55:39 +0000 (UTC) (envelope-from sgk@troutmask.apl.washington.edu) 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 9E412A4E; Mon, 24 Apr 2017 23:55:39 +0000 (UTC) (envelope-from sgk@troutmask.apl.washington.edu) Received: from troutmask.apl.washington.edu (localhost [127.0.0.1]) by troutmask.apl.washington.edu (8.15.2/8.15.2) with ESMTPS id v3ONRhmP054815 (version=TLSv1.2 cipher=DHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO); Mon, 24 Apr 2017 16:27:43 -0700 (PDT) (envelope-from sgk@troutmask.apl.washington.edu) Received: (from sgk@localhost) by troutmask.apl.washington.edu (8.15.2/8.15.2/Submit) id v3ONRhSI054814; Mon, 24 Apr 2017 16:27:43 -0700 (PDT) (envelope-from sgk) Date: Mon, 24 Apr 2017 16:27:43 -0700 From: Steve Kargl To: freebsd-numerics@freebsd.org Cc: freebsd-standards@freebsd.org Subject: Re: Implementation of half-cycle trignometric functions Message-ID: <20170424232743.GA54621@troutmask.apl.washington.edu> Reply-To: sgk@troutmask.apl.washington.edu References: <20170409220809.GA25076@troutmask.apl.washington.edu> <20170413171248.GA86780@troutmask.apl.washington.edu> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <20170413171248.GA86780@troutmask.apl.washington.edu> User-Agent: Mutt/1.7.2 (2016-11-26) X-BeenThere: freebsd-standards@freebsd.org X-Mailman-Version: 2.1.23 Precedence: list List-Id: Standards compliance List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Mon, 24 Apr 2017 23:55:39 -0000 On Thu, Apr 13, 2017 at 10:12:48AM -0700, Steve Kargl wrote: > On Sun, Apr 09, 2017 at 03:08:09PM -0700, Steve Kargl wrote: > > Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle > > trignometric functions cospi, sinpi, and tanpi. The attached > > patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited > > testing on the cospi and sinpi reveal a max ULP less than 0.89; > > while tanpi is more problematic with a max ULP less than 2.01 > > in the interval [0,0.5]. The algorithms used in these functions > > are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. > > > > Note 1. ISO/IEC TS 18661-4 says these funstions are guarded by > > a predefine macro. I have no idea or interest in what clang and > > gcc do with regards to this macro. I've put the functions behind > > __BSD_VISIBLE. > > > > Note 2. I no longer have access to a system with ld128 and > > adequate support to compile and test the ld128 implementations > > of these functions. Given the almost complete lack of input from > > others on improvements to libm, I doubt that anyone cares. If > > someone does care, the ld128 files contain a number of FIXME comments, > > and in particular, while the polynomial coefficients are given > > I did not update the polynomial algorithms to properly use the > > coefficients. > > > > The code is attached the bug reportr. > > > > https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=218514 > > > > While everyone is busy reviewing and testing the patch available > in bugzilla, I suspect some may be wondering about the inverse > half-cycle trignometric functions. I have worked out an algorithm > for asinpi[fl] and have a working implemenation of asinpif(x). > It will take a couple of weeks (due to limited available time) > before I can submit asinpi[fl], acospi[fl], and atanpi[fl], but > work is in progress. > I have what appears to be working versions of asinpi[fl]. It was suggested elsewhere that using an Estrin's method to sum the polynomial approximations instead of Horner's method may allow modern CPUs to better schedule generated code. I have implemented an Estrin's-like method for sinpi[l] and cospi[l], and indeed the generated code is faster on my Intel core2 duo with only a slight degradation in the observed max ULP. I'll post new versions to bugzilla in the near future. -- Steve 20161221 https://www.youtube.com/watch?v=IbCHE-hONow