From owner-freebsd-numerics@freebsd.org  Thu Mar  9 15:35:25 2017
Return-Path: <owner-freebsd-numerics@freebsd.org>
Delivered-To: freebsd-numerics@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 20036D05175
 for <freebsd-numerics@mailman.ysv.freebsd.org>;
 Thu,  9 Mar 2017 15:35:25 +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 0673636E
 for <freebsd-numerics@freebsd.org>; Thu,  9 Mar 2017 15:35:25 +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 v29FZO8g033424
 (version=TLSv1.2 cipher=DHE-RSA-AES256-GCM-SHA384 bits=256 verify=NO);
 Thu, 9 Mar 2017 07:35:24 -0800 (PST)
 (envelope-from sgk@troutmask.apl.washington.edu)
Received: (from sgk@localhost)
 by troutmask.apl.washington.edu (8.15.2/8.15.2/Submit) id v29FZNpC033420;
 Thu, 9 Mar 2017 07:35:23 -0800 (PST) (envelope-from sgk)
Date: Thu, 9 Mar 2017 07:35:23 -0800
From: Steve Kargl <sgk@troutmask.apl.washington.edu>
To: Bruce Evans <brde@optusnet.com.au>
Cc: freebsd-numerics@freebsd.org
Subject: Re: Bit twiddling question
Message-ID: <20170309153523.GA33379@troutmask.apl.washington.edu>
Reply-To: sgk@troutmask.apl.washington.edu
References: <20170308202417.GA23103@troutmask.apl.washington.edu>
 <20170309173152.F1269@besplex.bde.org>
 <20170309075236.GA30199@troutmask.apl.washington.edu>
 <20170309152307.GA32781@troutmask.apl.washington.edu>
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Disposition: inline
In-Reply-To: <20170309152307.GA32781@troutmask.apl.washington.edu>
User-Agent: Mutt/1.7.2 (2016-11-26)
X-BeenThere: freebsd-numerics@freebsd.org
X-Mailman-Version: 2.1.23
Precedence: list
List-Id: "Discussions of high quality implementation of libm functions."
 <freebsd-numerics.freebsd.org>
List-Unsubscribe: <https://lists.freebsd.org/mailman/options/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: <https://lists.freebsd.org/mailman/listinfo/freebsd-numerics>, 
 <mailto:freebsd-numerics-request@freebsd.org?subject=subscribe>
X-List-Received-Date: Thu, 09 Mar 2017 15:35:25 -0000

On Thu, Mar 09, 2017 at 07:23:07AM -0800, Steve Kargl wrote:
> 
>         if (ix < 0x43300000) {          /* 1 <= |x| < 0x1p52 */
>                 double volatile vx;
>                 uint32_t n;
>                 vx = ax + 0x1p52;
>                 vx = vx - 0x1p52;
>                 if (vx == ax) return(0);
>                 if (vx > UINT32_MAX) {   /* ax = m + n + r with m + n */
>                     vx -= UINT32_MAX;    /* m = UINT32_MAX.  n is in range */
>                     ax -= UINT32_MAX;    
> 				}
>                 n = (uint32_t)vx;
>                 ax = __compute_sinpi(ax - n);
>                 if (n & 1) ax = -ax;
>                 return ((hx & 0x80000000) ? -ax : ax);
>         }
> 

We don't even need to use UINT32_MAX.  We can do something
like

if (vx > 0x1p30) {
   vx -= 0x1p30;
   ax -= 0x1p30;
}

so there is no conversion from uint32_t to double.  We also
probably want to minimize access to a volatile, so we would
have y = vx - 0x1p52 and use y afterwards.

-- 
Steve
20161221 https://www.youtube.com/watch?v=IbCHE-hONow