From owner-cvs-src@FreeBSD.ORG Thu Feb 28 16:22:37 2008 Return-Path: Delivered-To: cvs-src@FreeBSD.org Received: from mx1.freebsd.org (mx1.freebsd.org [IPv6:2001:4f8:fff6::34]) by hub.freebsd.org (Postfix) with ESMTP id 24E49106566B; Thu, 28 Feb 2008 16:22:37 +0000 (UTC) (envelope-from bde@FreeBSD.org) Received: from repoman.freebsd.org (repoman.freebsd.org [IPv6:2001:4f8:fff6::29]) by mx1.freebsd.org (Postfix) with ESMTP id 0CF138FC14; Thu, 28 Feb 2008 16:22:37 +0000 (UTC) (envelope-from bde@FreeBSD.org) Received: from repoman.freebsd.org (localhost [127.0.0.1]) by repoman.freebsd.org (8.14.1/8.14.1) with ESMTP id m1SGMaBG050599; Thu, 28 Feb 2008 16:22:36 GMT (envelope-from bde@repoman.freebsd.org) Received: (from bde@localhost) by repoman.freebsd.org (8.14.1/8.14.1/Submit) id m1SGMaMt050598; Thu, 28 Feb 2008 16:22:36 GMT (envelope-from bde) Message-Id: <200802281622.m1SGMaMt050598@repoman.freebsd.org> From: Bruce Evans Date: Thu, 28 Feb 2008 16:22:36 +0000 (UTC) To: src-committers@FreeBSD.org, cvs-src@FreeBSD.org, cvs-all@FreeBSD.org X-FreeBSD-CVS-Branch: HEAD Cc: Subject: cvs commit: src/lib/msun/src e_rem_pio2.c e_rem_pio2f.c X-BeenThere: cvs-src@freebsd.org X-Mailman-Version: 2.1.5 Precedence: list List-Id: CVS commit messages for the src tree List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Thu, 28 Feb 2008 16:22:37 -0000 bde 2008-02-28 16:22:36 UTC FreeBSD src repository Modified files: lib/msun/src e_rem_pio2.c e_rem_pio2f.c Log: Fix and improve some magic numbers for the "medium size" case. e_rem_pio2.c: This case goes up to about 2**20pi/2, but the comment about it said that it goes up to about 2**19pi/2. It went too far above 2**pi/2, giving a multiplier fn with 21 significant bits in some cases. This would be harmful except for a numerical accident. It happens that the terms of the approximation to pi/2, when rounded to 33 bits so that multiplications by 20-bit fn's are exact, happen to be rounded to 32 bits so multiplications by 21-bit fn's are exact too, so the bug only complicates the error analysis (we might lose a bit of accuracy but have bits to spare). e_rem_pio2f.c: The bogus comment in e_rem_pio2.c was copied and the code was changed to be bug-for-bug compatible with it, except the limit was made 90 ulps smaller than necessary. The approximation to pi/2 was not modified except for discarding some of it. The same rough error analysis that justifies the limit of 2**20pi/2 for double precision only justifies a limit of 2**18pi/2 for float precision. We depended on exhaustive testing to check the magic numbers for float precision. More exaustive testing shows that we can go up to 2**28pi/2 using a 53+25 bit approximation to pi/2 for float precision, with a the maximum error for cosf() and sinf() unchanged at 0.5009 ulps despite the maximum error in rem_pio2f being ~0.25 ulps. Implement this. Revision Changes Path 1.18 +1 -1 src/lib/msun/src/e_rem_pio2.c 1.29 +3 -3 src/lib/msun/src/e_rem_pio2f.c