[Bug math/18039] [ldbl-128] acosl inaccurate

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https://sourceware.org/bugzilla/show_bug.cgi?id=18039

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=1d9ab20c14211abbf45514e63c190dfeec27fa5e

commit 1d9ab20c14211abbf45514e63c190dfeec27fa5e
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Thu Feb 26 21:06:34 2015 +0000

    Fix ldbl-128/ldbl-128ibm acosl inaccuracy (bug 18038, bug 18039).

    The ldbl-128 and ldbl-128ibm implementations of acosl have similar
    bugs, using a threshold of 0x1p-57L to determine when they just return
    pi/2.  Since the result pi/2 - asinl (x) is roughly pi/2 - x for small
    x, the relevant cut-off is actually x being < 0.5ulp of 1.  This patch
    fixes the implementations to use that cut-off and adds tests of small
    acos arguments.

    Tested for powerpc and mips64.  Also tested for x86_64 and x86; no
    ulps updates needed.

        [BZ #18038]
        [BZ #18039]
        * sysdeps/ieee754/ldbl-128/e_acosl.c (__ieee754_acosl): Only
        return pi/2 for arguments below 0x1p-113L.
        * sysdeps/ieee754/ldbl-128ibm/e_acosl.c (__ieee754_acosl): Only
        return pi/2 for arguments below 0x1p-106L.
        * math/auto-libm-test-in: Add more tests of acos.
        * math/auto-libm-test-out: Regenerated.

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

Summary of changes:
 ChangeLog                             |    9 +
 NEWS                                  |    2 +-
 math/auto-libm-test-in                |   31 ++
 math/auto-libm-test-out               |  775 +++++++++++++++++++++++++++++++++
 sysdeps/ieee754/ldbl-128/e_acosl.c    |    2 +-
 sysdeps/ieee754/ldbl-128ibm/e_acosl.c |    2 +-
 6 files changed, 818 insertions(+), 3 deletions(-)

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