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[2001:8b0:bf73:93f7::51bb:e332]) by smtp.gmail.com with ESMTPSA id i6-20020a05600c354600b004107686650esm2965177wmq.36.2024.02.16.09.32.01 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Fri, 16 Feb 2024 09:32:01 -0800 (PST) Received: from jsm28 (helo=localhost) by digraph.polyomino.org.uk with local-esmtp (Exim 4.95) (envelope-from ) id 1rb248-002fEQ-T1; Fri, 16 Feb 2024 17:32:00 +0000 Date: Fri, 16 Feb 2024 17:32:00 +0000 (UTC) From: Joseph Myers To: Vincent Lefevre cc: libc-alpha@sourceware.org Subject: Re: document the fact that "Known Maximum Errors" might not be maximal In-Reply-To: <20240216123950.GC3653@qaa.vinc17.org> Message-ID: References: <20240216094334.GA3653@qaa.vinc17.org> <20240216102258.GB3653@qaa.vinc17.org> <20240216123950.GC3653@qaa.vinc17.org> MIME-Version: 1.0 X-Mimecast-Spam-Score: 0 X-Mimecast-Originator: redhat.com Content-Type: text/plain; charset=US-ASCII X-Spam-Status: No, score=-4.1 required=5.0 tests=BAYES_00,DKIMWL_WL_HIGH,DKIM_SIGNED,DKIM_VALID,DKIM_VALID_AU,DKIM_VALID_EF,RCVD_IN_DNSWL_NONE,RCVD_IN_MSPIKE_H2,SPF_HELO_NONE,SPF_NONE,TXREP,T_SCC_BODY_TEXT_LINE autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org List-Id: On Fri, 16 Feb 2024, Vincent Lefevre wrote: > If I understand correctly, the *intent* is to give an error bounded > by 3 ulp, i.e. an error up to 3 ulp is not something that the user > should expect to be "fixed". The intent is that the functions should be both "accurate" (where more details of the precise goals are given in the manual - see the first several paragraphs of the "Errors in Math Functions" section) and "fast". 3 ulp isn't a specific intent. The testsuite always treats any error above 9 ulp (16 ulp for IBM long double) as a bug. In practice I think it's likely that most or all of the functions with errors above 1 ulp for round-to-nearest could be improved (other than for IBM long double) to have errors of at most 1 ulp without making them any slower, using better implementations. (The definition of ulp used by the testsuite and the table in the manual compares to the correctly rounded result, *not* to the mathematically precise result. So fractional ulp values are not possible, except for the special case where the result returned by the function has a lower exponent than the correctly rounded result.) (The main cases that would be genuinely hard to get down to low errors for all arguments are the cpow, jn and yn functions.) -- Joseph S. Myers josmyers@redhat.com