From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 44446 invoked by alias); 12 Mar 2018 15:36:47 -0000 Mailing-List: contact libc-alpha-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: libc-alpha-owner@sourceware.org Received: (qmail 43949 invoked by uid 89); 12 Mar 2018 15:36:46 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=-2.8 required=5.0 tests=AWL,BAYES_00,RCVD_IN_DNSWL_NONE,SPF_HELO_PASS,SPF_PASS autolearn=ham version=3.3.2 spammy= X-HELO: EUR02-VE1-obe.outbound.protection.outlook.com From: Wilco Dijkstra To: Joseph Myers , Steve Ellcey CC: Zack Weinberg , =?iso-8859-2?Q?Ond=F8ej_B=EDlka?= , Siddhesh Poyarekar , "libc-alpha@sourceware.org" , nd Subject: Re: [PATCH 2/6] Remove slow paths from sin/cos Date: Mon, 12 Mar 2018 15:36:00 -0000 Message-ID: References: <1520636722.6774.157.camel@cavium.com>, In-Reply-To: authentication-results: spf=none (sender IP is ) smtp.mailfrom=Wilco.Dijkstra@arm.com; x-ms-publictraffictype: Email x-microsoft-exchange-diagnostics: 1;DB6PR0801MB1975;7:59IRqGS1B6uvKaS8Oeg4w68NXfbQQcz8O5OvJdviCqC/gC8vN+vZZ/BIQLZR1qyGzLAUX3ErESZK8v8Ea3naJ7MDxCJq/p25X7uBwkMoZCMBMODvqiNW7VDqfYZYUKhjm1v8jVXWm4YfpcLtb62xcRikYZeGfTodBuAuVkrZeY088DTLRSMIVeMRT/PNcSHkTseAdkOOyBu51yY2FsirTPuqQq1M34m51QD0NnvLGZBitC5tsl1Xsy7BbJPw4ewq x-ms-exchange-antispam-srfa-diagnostics: SSOS; x-ms-office365-filtering-ht: Tenant x-ms-office365-filtering-correlation-id: a544bc57-a921-401d-8a83-08d5882f0db6 x-microsoft-antispam: UriScan:;BCL:0;PCL:0;RULEID:(7020095)(4652020)(48565401081)(5600026)(4604075)(3008032)(4534165)(4627221)(201703031133081)(201702281549075)(2017052603328)(7153060)(7193020);SRVR:DB6PR0801MB1975; x-ms-traffictypediagnostic: DB6PR0801MB1975: nodisclaimer: True x-microsoft-antispam-prvs: x-exchange-antispam-report-test: UriScan:; x-exchange-antispam-report-cfa-test: BCL:0;PCL:0;RULEID:(8211001083)(6040522)(2401047)(8121501046)(5005006)(3002001)(93006095)(93001095)(10201501046)(3231220)(944501244)(52105095)(6055026)(6041310)(20161123564045)(201703131423095)(201702281528075)(20161123555045)(201703061421075)(201703061406153)(20161123562045)(20161123560045)(20161123558120)(6072148)(201708071742011);SRVR:DB6PR0801MB1975;BCL:0;PCL:0;RULEID:;SRVR:DB6PR0801MB1975; x-forefront-prvs: 06098A2863 x-forefront-antispam-report: SFV:NSPM;SFS:(10009020)(396003)(376002)(346002)(39380400002)(366004)(39860400002)(199004)(189003)(76176011)(6116002)(6436002)(5660300001)(53936002)(3846002)(316002)(81166006)(2950100002)(54906003)(68736007)(6506007)(7736002)(3280700002)(99286004)(86362001)(8656006)(305945005)(105586002)(478600001)(106356001)(81156014)(97736004)(33656002)(9686003)(102836004)(8936002)(2900100001)(8676002)(66066001)(4326008)(110136005)(74316002)(72206003)(186003)(2906002)(5250100002)(6246003)(7696005)(25786009)(26005)(55016002)(229853002)(14454004)(3660700001)(59450400001);DIR:OUT;SFP:1101;SCL:1;SRVR:DB6PR0801MB1975;H:DB6PR0801MB2053.eurprd08.prod.outlook.com;FPR:;SPF:None;PTR:InfoNoRecords;A:1;MX:1;LANG:en; received-spf: None (protection.outlook.com: arm.com does not designate permitted sender hosts) x-microsoft-antispam-message-info: bRX8SvvriOXcw0iCSt7hMAXny4Qo7QutnWVDg6yoDAH2K692IwLEBQYUpGuLq8TLtj+ZCQHNSk8ScIvSUre97H+skXajzd3Cv0OTZr6jqW6QSB0ewvzHwdj9IH+Xxo2/fCXYPO0j4OC9sL7tPcOBdcLffyEFB+olS76XoqYIUb0YiZpSlV9tMLlTxTZxSVMJbSRxJIFbTSPSyvHQdHjXByueu90MFWCBKVAIqtzyXiVOQ0pchFdXEFNFOU1/KPSbuMLd3VD6P/KWcgBeE73Zu2lfJXUqheDnAU/ESetwt7ZMfxBQvEUOAhtf1PE5dLO1B5HBgzraJShDt/mvOq718Q== spamdiagnosticoutput: 1:99 spamdiagnosticmetadata: NSPM Content-Type: text/plain; charset="iso-8859-2" Content-Transfer-Encoding: quoted-printable MIME-Version: 1.0 X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-Network-Message-Id: a544bc57-a921-401d-8a83-08d5882f0db6 X-MS-Exchange-CrossTenant-originalarrivaltime: 12 Mar 2018 15:36:41.6450 (UTC) X-MS-Exchange-CrossTenant-fromentityheader: Hosted X-MS-Exchange-CrossTenant-id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-Transport-CrossTenantHeadersStamped: DB6PR0801MB1975 X-SW-Source: 2018-03/txt/msg00287.txt.bz2 Joseph Myers wrote: > Yes.=A0 A floating-point number represents a particular real number, not = an=20 > interval, so all the usual accuracy goals (of results within a few ulps o= f=20 > the correct answer) apply for large inputs (but performance is not a=20 > concern for those inputs).=A0 Only for IBM long double is this relaxed, t= o=20 > treat values not representable in 106 mantissa bits as if they do=20 > represent intervals. Though these patches keep the ULP accuracy across the full range as is,=20 we could agree on higher ULP errors for large/huge range reduction cases=20 in the future. The main complexity is for certain rare inputs which happen = to be extremely close to an integer multiple of PI/2, and those few cases mean you need significant extra work to guarantee 0.5 ULP error bound on range reduction. Wilco