[Bug math/16356] Bad results from x86 / x86_64 expl in round-upward mode

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http://sourceware.org/bugzilla/show_bug.cgi?id=16356

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=5b0626b9c50e69fe4d7dce90199d78f398c249b1

commit 5b0626b9c50e69fe4d7dce90199d78f398c249b1
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Sat Dec 21 13:07:16 2013 +0000

    Fix x86 / x86_64 expl / expl10l wild results in directed rounding modes
(bug 16356).

    This patch fixes bug 16356, bad results from x86 / x86_64 expl /
    exp10l in directed rounding modes, the most serious of the bugs shown
    up by my patch expanding libm test coverage.  When I fixed bug 16293,
    I thought it was only necessary to set round-to-nearest when using
    frndint in expm1 functions, because in other cases the cancellation
    error from having the resulting fractional part close to 1 or -1 would
    not be significant.  However, in expl and exp10l, the way the final
    fractional part gets computed (something more complicated than a
    simple subtraction, because more precision is needed than you'd get
    that way) can result in a value outside the range [-1, 1] when the
    argument to frndint was very close to an integer and was rounded the
    "wrong" way because of the rounding mode - and the f2xm1 instruction
    has undefined results if its argument is outside [-1, 1], so resulting
    in the large errors seen.  So this patch removes the USE_AS_EXPM1L
    conditionals on the round-to-nearest settings, so all of expl, expm1l
    and exp10l now get round-to-nearest used for frndint (meaning the
    final fractional part can at most be slightly above 0.5 in
    magnitude).  Associated tests of exp and exp10 are added and testing
    of exp10 in directed rounding modes enabled.

    Tested x86_64 and x86 and ulps updated accordingly.

        * sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL): Also set
        round-to-nearest for [!USE_AS_EXPM1L].
        * sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL): Likewise.
        * math/auto-libm-test-in: Do not expect cosh tests to fail.  Add
        more tests of exp and exp10.  Expect some exp10 tests to miss
        exceptions or fail in directed rounding modes.
        * math/auto-libm-test-out: Regenerated.
        * math/libm-test.inc (exp10_tonearest_test_data): New array.
        (exp10_test_tonearest): New function.
        (exp10_towardzero_test_data): New array.
        (exp10_test_towardzero): New function.
        (exp10_downward_test_data): New array.
        (exp10_test_downward): New function.
        (exp10_upward_test_data): New array.
        (exp10_test_upward): New function.
        (main): Call the new functions.
        * sysdeps/i386/fpu/libm-test-ulps: Update.
        * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

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

Summary of changes:
 ChangeLog                         |   22 +
 NEWS                              |    2 +-
 math/auto-libm-test-in            |   27 +-
 math/auto-libm-test-out           | 1254 ++++++++++++++++++++++---------------
 math/libm-test.inc                |   60 ++
 sysdeps/i386/fpu/e_expl.S         |    4 -
 sysdeps/i386/fpu/libm-test-ulps   |  114 ++++-
 sysdeps/x86_64/fpu/e_expl.S       |    4 -
 sysdeps/x86_64/fpu/libm-test-ulps |  122 ++++-
 9 files changed, 1059 insertions(+), 550 deletions(-)

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