[Bug math/15062] New: casinh spurious underflows (away from [-i,i])

["jsm28 at gcc dot gnu.org" <sourceware-bugzilla at sourceware dot org>]

http://sourceware.org/bugzilla/show_bug.cgi?id=15062

             Bug #: 15062
           Summary: casinh spurious underflows (away from [-i,i])
           Product: glibc
           Version: 2.17
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
        AssignedTo: unassigned@sourceware.org
        ReportedBy: jsm28@gcc.gnu.org
    Classification: Unclassified


The computation of casinh using log(z + sqrt(1  + z*z)) suffers from spurious
underflows when the complex sqrt underflows even though neither the real nor
the imaginary part of the final result would underflow.  The same similarly
applies to casin and cacos, implemented in terms of casinh.  Working on a
patch.

This bug is specifically about such underflows away from the line from -i to i
(where the real part of the result is 0); there are probably also such
underflows close to that line, but they will need fixing separately along with
the general issues of inaccuracy close to that line (bug 10357).

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