From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: by sourceware.org (Postfix, from userid 48) id F37523858405; Tue, 26 Oct 2021 22:35:33 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org F37523858405 From: "mwelinder at gmail dot com" To: glibc-bugs@sourceware.org Subject: [Bug manual/28502] New: Accuracy claim for complex functions Date: Tue, 26 Oct 2021 22:35:33 +0000 X-Bugzilla-Reason: CC X-Bugzilla-Type: new X-Bugzilla-Watch-Reason: None X-Bugzilla-Product: glibc X-Bugzilla-Component: manual X-Bugzilla-Version: 2.31 X-Bugzilla-Keywords: X-Bugzilla-Severity: minor X-Bugzilla-Who: mwelinder at gmail dot com X-Bugzilla-Status: UNCONFIRMED X-Bugzilla-Resolution: X-Bugzilla-Priority: P2 X-Bugzilla-Assigned-To: unassigned at sourceware dot org X-Bugzilla-Target-Milestone: --- X-Bugzilla-Flags: X-Bugzilla-Changed-Fields: bug_id short_desc product version bug_status bug_severity priority component assigned_to reporter cc target_milestone Message-ID: Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable X-Bugzilla-URL: http://sourceware.org/bugzilla/ Auto-Submitted: auto-generated MIME-Version: 1.0 X-BeenThere: glibc-bugs@sourceware.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Glibc-bugs mailing list List-Unsubscribe: , List-Archive: List-Help: List-Subscribe: , X-List-Received-Date: Tue, 26 Oct 2021 22:35:34 -0000 https://sourceware.org/bugzilla/show_bug.cgi?id=3D28502 Bug ID: 28502 Summary: Accuracy claim for complex functions Product: glibc Version: 2.31 Status: UNCONFIRMED Severity: minor Priority: P2 Component: manual Assignee: unassigned at sourceware dot org Reporter: mwelinder at gmail dot com CC: mtk.manpages at gmail dot com Target Milestone: --- See math.texi, "Errors in Math Functions". @item Each function with a floating-point result behaves as if it computes an infinite-precision result that is within a few ulp (in both real and complex parts, for functions with complex results) of the mathematically correct value of the function[...] This would be quite stellar performance for complex functions, if true. It= is not true. Bug 14473 has a few examples, notably I^(2+I) --> -0.20788 + 2.54571e-17 I in which the imaginary part -- which should be 0 -- is off by 2^60ulp or something like that. I bring it up here as a documentation bug because I think the per-coordinate accuracy goal is the wrong target for a function like cpow. It's a non-tri= vial topic, but something involving the complex absolute value of the difference between the theoretical and observed results compared to the absolute value= of the theoretical result seems right. A no-error guarantee for creal, cimag, and conj would make sense too. Note that the table of known errors (as seen at the bottom of https://www.gnu.org/software/libc/manual/html_node/Errors-in-Math-Functions= .html) claims a few ulp for cpow which is way off. Bug 14473 also has the example I^(2^53+I) --> 0.177058 + -0.108924 i which is off by something like 2^52ulp in the real part. --=20 You are receiving this mail because: You are on the CC list for the bug.=