[Bug math/18046] [ldbl-96] atanhl inaccurate

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https://sourceware.org/bugzilla/show_bug.cgi?id=18046

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=2ca725c594e0c186d928dc0823be7d8b5976112c

commit 2ca725c594e0c186d928dc0823be7d8b5976112c
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Fri Feb 27 17:48:37 2015 +0000

    Fix ldbl-96, ldbl-128ibm atanhl inaccuracy (bug 18046, bug 18047).

    The threshold in ldbl-96 atanhl for when to return the argument,
    0x1p-28, is a bit too big, and that in ldbl-128ibm atanhl is much too
    big (the relevant condition being x^3/3 being < 0.5ulp of x),
    resulting in errors a bit above the limits of those considered
    acceptable in glibc in the ldbl-96 case, and in large errors in the
    ldbl-128ibm case.  This patch changes those implementations to use
    more appropriate thresholds and adds tests around the thresholds for
    various formats.

    Tested for x86_64, x86 and powerpc.  x86_64 and x86 ulps updated
    accordingly.

        [BZ #18046]
        [BZ #18047]
        * sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Use
        0x1p-56L as threshold for just returning the argument.
        * sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Use
        0x1p-32L as threshold for just returning the argument.
        * math/auto-libm-test-in: Add more tests of atanh.
        * math/auto-libm-test-out: Regenerated.
        * sysdeps/i386/fpu/libm-test-ulps: Update.
        * sysdeps/x86_64/fpu/libm-test-ulp: Likewise.

-----------------------------------------------------------------------

Summary of changes:
 ChangeLog                              |   13 +
 NEWS                                   |    3 +-
 math/auto-libm-test-in                 |   31 ++
 math/auto-libm-test-out                |  875 ++++++++++++++++++++++++++++++++
 sysdeps/i386/fpu/libm-test-ulps        |    2 +
 sysdeps/ieee754/ldbl-128ibm/e_atanhl.c |    2 +-
 sysdeps/ieee754/ldbl-96/e_atanhl.c     |    4 +-
 sysdeps/x86_64/fpu/libm-test-ulps      |    4 +
 8 files changed, 930 insertions(+), 4 deletions(-)

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