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From: "jsm28 at gcc dot gnu.org" <sourceware-bugzilla@sourceware.org>
To: glibc-bugs@sourceware.org
Subject: [Bug math/15416] New: catan, catanh inaccuracy from atan2
Date: Mon, 29 Apr 2013 16:25:00 -0000
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http://sourceware.org/bugzilla/show_bug.cgi?id=15416

             Bug #: 15416
           Summary: catan, catanh inaccuracy from atan2
           Product: glibc
           Version: 2.17
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: unassigned@sourceware.org
        ReportedBy: jsm28@gcc.gnu.org
    Classification: Unclassified


When catan computes __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x,
den), the value of den may be inaccurate when close to 0, resulting in an
inaccurate real part of the result when __real__ x is also small.  For example,
catan (0x1p-27 + 1.0i) gives a result with real part 0.785398163397448279 on
x86_64, which is only accurate to 8 decimal places, about half the precision
expected (the exact value is 0.785398165260093458846617868453411006955...). 
The same applies to catanh.

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