[Bug manual/28502] New: Accuracy claim for complex functions

[Bug manual/28502] New: Accuracy claim for complex functions

[mwelinder at gmail dot com]

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.

[Bug manual/28502] Accuracy claim for complex functions

[joseph at codesourcery dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=28502

--- Comment #1 from joseph at codesourcery dot com <joseph at codesourcery dot com> ---
The documentation says:

  Instead, the goals for
  accuracy of functions without fully specified results are as follows;
  some functions have bugs meaning they do not meet these goals in all
  cases.

The "some functions have bugs ..." is intended to cover cases such as cpow 
and jn.

Also, the table is explicitly only for errors covered by the existing 
tests in the testsuite.

-- 
You are receiving this mail because:
You are on the CC list for the bug.

[Bug manual/28502] Accuracy claim for complex functions

[joseph at codesourcery dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=28502

--- Comment #2 from joseph at codesourcery dot com <joseph at codesourcery dot com> ---
creal, cimag and conj are covered by the "Except for certain functions 
such as @code{sqrt}, @code{fma} and @code{rint} whose results are fully 
specified by reference to corresponding IEEE 754 floating-point 
operations, and conversions between strings and floating point" text.  
(For the exact list of covered functions, look at which functions have 1 
as the second argument to ALL_RM_TEST in their tests.)

-- 
You are receiving this mail because:
You are on the CC list for the bug.