From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.4.2 (2018-09-13) on dcvr.yhbt.net X-Spam-Level: X-Spam-Status: No, score=-3.9 required=3.0 tests=AWL,BAYES_00, HEADER_FROM_DIFFERENT_DOMAINS,MAILING_LIST_MULTI,SPF_HELO_PASS, SPF_PASS shortcircuit=no autolearn=ham autolearn_force=no version=3.4.2 Received: from sourceware.org (server2.sourceware.org [IPv6:2620:52:3:1:0:246e:9693:128c]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits) key-exchange X25519 server-signature RSA-PSS (4096 bits) server-digest SHA256) (No client certificate requested) by dcvr.yhbt.net (Postfix) with ESMTPS id 562791F5AE for ; Mon, 27 Jul 2020 21:35:39 +0000 (UTC) Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id F09BB3857001; Mon, 27 Jul 2020 21:35:37 +0000 (GMT) Received: from esa2.mentor.iphmx.com (esa2.mentor.iphmx.com [68.232.141.98]) by sourceware.org (Postfix) with ESMTPS id E556D3857C55 for ; Mon, 27 Jul 2020 21:35:35 +0000 (GMT) DMARC-Filter: OpenDMARC Filter v1.3.2 sourceware.org E556D3857C55 Authentication-Results: sourceware.org; dmarc=none (p=none dis=none) header.from=codesourcery.com Authentication-Results: sourceware.org; spf=pass smtp.mailfrom=joseph_myers@mentor.com IronPort-SDR: lCaQ0FfuOb9caAmOKmmdOnTzo4WqG5igfbNHOk5ZurwRqIx4SbhMOSka9Ukly0hhHnFnP++JXo 3YGPbt5egbjVONTsnMB3i7lF6gNm0baUm3eSvgG2/laPbNdh+xcOCwMWcoxQVqOjrpkXrkSp2R YfPwcM26KN5uks3zR1r+9TBpCxNDbLyA6JC135sBCjGNh8gf7B0lvHhEk9LwCbBc4J5oRF3gMS W01Po3G+7WKQSmfCnD2guyKnQ4WQu41la0CgTLw51sbr5cpoQ+ao9StiP7vizgRB7oK3wubl1Z Ukc= X-IronPort-AV: E=Sophos;i="5.75,403,1589270400"; d="scan'208";a="51351529" Received: from orw-gwy-01-in.mentorg.com ([192.94.38.165]) by esa2.mentor.iphmx.com with ESMTP; 27 Jul 2020 13:35:34 -0800 IronPort-SDR: If1Ny5kf8Iw9TX0s2U92dxr/9kYFCAxzZBo35SkJ9LZ0f6UuD8dT2Im3csJ+2uRfyT+6hvfZEF haYx9EtXO5xd9bjtDHLhbAUJm1+T0BYvNkfnwYmNAWcgbuI1S2DGEe/qnwhHiN6UunMzpKqrN4 y1F2DgsPWlGheg8U+sWtsWzAPW9pO2OojzhVZDAtt9D2jCrEwDrkFr02rHrkXkmhlZCg6Dcnb+ OoL5Mr89FhBejbSTxZ9eA4wmdhC9XPB/fctJPDHO9erZr70oUnFumQe+GSXr/Xe55R3Mi+CLw9 6+g= Date: Mon, 27 Jul 2020 21:35:29 +0000 From: Joseph Myers X-X-Sender: jsm28@digraph.polyomino.org.uk To: Paul Zimmermann Subject: Re: fix inaccuracy of j0f for x >= 2^127 when sin(x)+cos(x) is tiny In-Reply-To: Message-ID: References: User-Agent: Alpine 2.21 (DEB 202 2017-01-01) MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" X-Originating-IP: [137.202.0.90] X-ClientProxiedBy: SVR-IES-MBX-07.mgc.mentorg.com (139.181.222.7) To svr-ies-mbx-01.mgc.mentorg.com (139.181.222.1) X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Cc: libc-alpha@sourceware.org Errors-To: libc-alpha-bounces@sourceware.org Sender: "Libc-alpha" On Mon, 27 Jul 2020, Paul Zimmermann wrote: > + float x0 = 3.153646966e+38f; > + float y = x - x0; /* exact */ > + /* sin(y) = sin(x)*cos(x0)-cos(x)*sin(x0) */ > + z = __sinf (y); > + float eps = 8.17583368e-8f; > + /* cos(x0) ~ -sin(x0) + eps */ > + z += eps * __cosf (x); > + /* now z ~ (sin(x)-cos(x))*cos(x0) */ > + float cosx0 = -0.707106740f; In new code we generally prefer to use hex float constants in such cases where a specific floating-point value is wanted. -- Joseph S. Myers joseph@codesourcery.com