[Bug math/16293] x86 / x86_64 expm1 inaccurate near 0 in directed rounding modes

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http://sourceware.org/bugzilla/show_bug.cgi?id=16293

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=f88acd39da2a509081e541b84ecbf204ef20f9e8

commit f88acd39da2a509081e541b84ecbf204ef20f9e8
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Thu Dec 19 13:36:10 2013 +0000

    Fix x86/x86_64 expm1 inaccuracy near 0 in directed rounding modes (bug
16293).

    Bug 16293 is inaccuracy of x86/x86_64 versions of expm1, near 0 in
    directed rounding modes, that arises from frndint rounding the
    exponent to 1 or -1 instead of 0, resulting in large cancellation
    error.  This inaccuracy in turn affects other functions such as sinh
    that use expm1.  This patch fixes the problem by setting
    round-to-nearest mode temporarily around the affected calls to
    frndint.  I don't think this is needed for other uses of frndint, such
    as in exp itself, as only for expm1 is the cancellation error
    significant.

    Tested x86_64 and x86 and ulps updated accordingly.

        * sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Set
        round-to-nearest mode when using frndint.
        * sysdeps/i386/fpu/s_expm1.S (__expm1): Likewise.
        * sysdeps/i386/fpu/s_expm1f.S (__expm1f): Likewise.
        * sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
        Likewise.
        * math/auto-libm-test-in: Add more tests of expm1.  Do not expect
        sinh test to fail.
        * math/auto-libm-test-out: Regenerated.
        * math/libm-test.inc (TEST_COND_x86_64): Remove macro.
        (TEST_COND_x86): Likewise.
        (expm1_tonearest_test_data): New array.
        (expm1_test_tonearest): New function.
        (expm1_towardzero_test_data): New array.
        (expm1_test_towardzero): New function.
        (expm1_downward_test_data): New array.
        (expm1_test_downward): New function.
        (expm1_upward_test_data): New array.
        (expm1_test_upward): New function.
        (main): Run the new test functions.
        * sysdeps/i386/fpu/libm-test-ulps: Update.
        * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

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

Summary of changes:
 ChangeLog                         |   24 ++
 NEWS                              |    2 +-
 math/auto-libm-test-in            |   19 ++-
 math/auto-libm-test-out           |  450 ++++++++++++++++++++++++++++++++++--
 math/libm-test.inc                |   72 +++++-
 sysdeps/i386/fpu/e_expl.S         |   15 ++
 sysdeps/i386/fpu/libm-test-ulps   |  375 ++++++++++++++++++++++++++++++
 sysdeps/i386/fpu/s_expm1.S        |   11 +
 sysdeps/i386/fpu/s_expm1f.S       |   11 +
 sysdeps/x86_64/fpu/e_expl.S       |   11 +
 sysdeps/x86_64/fpu/libm-test-ulps |  319 ++++++++++++++++++++++++++
 11 files changed, 1269 insertions(+), 40 deletions(-)

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