[Bug math/12786] New: cacosh sometimes returning wrong result for real values between -1 and 1

[Bug math/12786] New: cacosh sometimes returning wrong result for real values between -1 and 1

[bert.barbe at oracle dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

           Summary: cacosh sometimes returning wrong result for real
                    values between -1 and 1
           Product: glibc
           Version: 2.12
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: aj@suse.de
        ReportedBy: bert.barbe@oracle.com


Created attachment 5738
  --> http://sourceware.org/bugzilla/attachment.cgi?id=5738
test program

After the fix for http://sourceware.org/bugzilla/show_bug.cgi?id=2182
cacosh, cacoshf and cacoshl can return results with the wrong sign when
the argument is a real value between -1 and 1.
This is because due to rounding errors, the real part of the result is a small
negative value instead of 0. The fix for bz2182 will change the sign of the
result because the real part is negative.

Note that the formula w=clogf(z+ csqrtf(z+1) * csqrtf (z -1)) of other
implementations does give the correct sign right away.

Some examples on a x86_64 linux , Intel(R) Xeon(R) CPU  5160 ,
glibc-2.12-1.7.el6.x86_64:

*** z=-0.680000 + 0.000000*i   cacoshf(z)=+5.960464e-08  -2.318559e+00 *i
*** z=-0.670000 + 0.000000*i   cacoshf(z)=+5.960464e-08  -2.305006e+00 *i
*** z=-0.580000 + 0.000000*i   cacoshf(z)=+5.960464e-08  -2.189526e+00 *i
*** z=-0.570000 + 0.000000*i   cacoshf(z)=+5.960464e-08  -2.177303e+00 *i

Attached is a test program that will print the cacosh values for real arguments
between -1 and +1 , at interval 0.01 and indicate the results with a wrong sign
with "***"

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[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[bert.barbe at oracle dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

--- Comment #1 from Bert Barbe <bert.barbe at oracle dot com> 2011-05-20 13:31:06 UTC ---
Created attachment 5740
  --> http://sourceware.org/bugzilla/attachment.cgi?id=5740
proposed patch for 2.13 release

Also verified problem in glibc release 2.13. Proposed patch for 2.13 for
cacoshf. If agreed, similar patch needs to be applied to cacosh and cacoshl.

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[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[carlos at codesourcery dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

Carlos O'Donell <carlos at codesourcery dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
           Keywords|                            |glibc_2.13
                 CC|                            |carlos at codesourcery dot
                   |                            |com

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[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[carlos at systemhalted dot org]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

Carlos O'Donell <carlos at systemhalted dot org> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |carlos at systemhalted dot
                   |                            |org

--- Comment #2 from Carlos O'Donell <carlos at systemhalted dot org> 2011-06-09 15:18:14 UTC ---
Has this been fixed in trunk yet?

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[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[kreckel at ginac dot de]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

Richard B. Kreckel <kreckel at ginac dot de> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |kreckel at ginac dot de

--- Comment #3 from Richard B. Kreckel <kreckel at ginac dot de> 2011-11-23 09:04:57 UTC ---
(In reply to comment #1)
> Created attachment 5740 [details]
> proposed patch for 2.13 release

That patch only fixes a symptom and not the cause. A better patch has been
attached to BZ 13305.

The rounding errors in cacosh[fl] are a completely different problem and should
be analyzed and fixed separately. They are due to the argument of the final
clog(y) being close to 1. The instability of log(1+x) for small x are
well-known and have lead to the log1p function. I believe the rounding errors
in cacosh[fl] would go away if the clog(y) would be replaced by clog1p(y), if
that would exist.

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[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[drepper.fsp at gmail dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

Ulrich Drepper <drepper.fsp at gmail dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
   Attachment #5738|application/octet-stream    |text/plain
          mime type|                            |

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[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[drepper.fsp at gmail dot com]

http://sourceware.org/bugzilla/show_bug.cgi?id=12786

Ulrich Drepper <drepper.fsp at gmail dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|NEW                         |RESOLVED
                 CC|                            |drepper.fsp at gmail dot
                   |                            |com
         Resolution|                            |DUPLICATE

--- Comment #4 from Ulrich Drepper <drepper.fsp at gmail dot com> 2011-12-23 16:02:28 UTC ---
Already fixed in another BZ

*** This bug has been marked as a duplicate of bug 13305 ***

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[Bug math/12786] cacosh sometimes returning wrong result for real values between -1 and 1

[fweimer at redhat dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=12786

Florian Weimer <fweimer at redhat dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
              Flags|                            |security-

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