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* [Bug manual/28502] New: Accuracy claim for complex functions
@ 2021-10-26 22:35 mwelinder at gmail dot com
2021-10-27 0:05 ` [Bug manual/28502] " joseph at codesourcery dot com
2021-10-27 0:08 ` joseph at codesourcery dot com
0 siblings, 2 replies; 3+ messages in thread
From: mwelinder at gmail dot com @ 2021-10-26 22:35 UTC (permalink / raw)
To: glibc-bugs
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.
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2021-10-26 22:35 [Bug manual/28502] New: Accuracy claim for complex functions mwelinder at gmail dot com
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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