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From: "mwelinder at gmail dot com" <sourceware-bugzilla@sourceware.org> To: glibc-bugs@sourceware.org Subject: [Bug manual/28502] New: Accuracy claim for complex functions Date: Tue, 26 Oct 2021 22:35:33 +0000 [thread overview] Message-ID: <bug-28502-131@http.sourceware.org/bugzilla/> (raw) https://sourceware.org/bugzilla/show_bug.cgi?id=28502 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-trivial 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. -- You are receiving this mail because: You are on the CC list for the bug.
next reply other threads:[~2021-10-26 22:35 UTC|newest] Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top 2021-10-26 22:35 mwelinder at gmail dot com [this message] 2021-10-27 0:05 ` [Bug manual/28502] " joseph at codesourcery dot com 2021-10-27 0:08 ` joseph at codesourcery dot com
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