[Bug math/15319] Missing underflow exceptions from atan / atan2

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https://sourceware.org/bugzilla/show_bug.cgi?id=15319

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=4629c866ad79167d60ca9bf263d871eabb59d3d9

commit 4629c866ad79167d60ca9bf263d871eabb59d3d9
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Wed Feb 18 21:10:49 2015 +0000

    Fix atan / atan2 missing underflows (bug 15319).

    This patch fixes bug 15319, missing underflows from atan / atan2 when
    the result of atan is very close to its small argument (or that of
    atan2 is very close to the ratio of its arguments, which may be an
    exact division).

    The usual approach of doing an underflowing computation if the
    computed result is subnormal is followed.  For 32-bit x86, there are
    extra complications: the inline __ieee754_atan2 in bits/mathinline.h
    needs to be disabled for float and double because other libm functions
    using it generally rely on getting proper underflow exceptions from
    it, while the out-of-line functions have to remove excess range and
    precision from the underflowing result so as to return an exact 0 in
    the case where errno should be set for underflow to 0.  (The failures
    I saw without that are similar to those Carlos reported for other
    functions, where I haven't seen a response to
    <https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>
    confirming if my diagnosis is correct.  Arguably all libm functions
    with float and double returns should remove excess range and
    precision, but that's a separate matter.)

    The x86_64 long double case reported in a comment in bug 15319 is not
    a bug (it's an argument of LDBL_MIN, and x86_64 is an after-rounding
    architecture so the correct IEEE result is not to raise underflow in
    the given rounding mode, in addition to treating the result as an
    exact LDBL_MIN being within the newly clarified documentation of
    accuracy goals).  I'm presuming that the fpatan instruction can be
    trusted to raise appropriate exceptions when the (long double) result
    underflows (after rounding) and so no changes are needed for x86 /
    x86_64 long double functions here; empirically this is the case for
    the cases covered in the testsuite, on my system.

    Tested for x86_64, x86, powerpc and mips64.  Only 32-bit x86 needs
    ulps updates (for the changes to inlines meaning some functions no
    longer get excess precision from their __ieee754_atan2* calls).

        [BZ #15319]
        * sysdeps/i386/fpu/e_atan2.S (dbl_min): New object.
        (MO): New macro.
        (__ieee754_atan2): For results with small absolute value, force
        underflow exception and remove excess range and precision from
        return value.
        * sysdeps/i386/fpu/e_atan2f.S (flt_min): New object.
        (MO): New macro.
        (__ieee754_atan2f): For results with small absolute value, force
        underflow exception and remove excess range and precision from
        return value.
        * sysdeps/i386/fpu/s_atan.S (dbl_min): New object.
        (MO): New macro.
        (__atan): For results with small absolute value, force underflow
        exception and remove excess range and precision from return value.
        * sysdeps/i386/fpu/s_atanf.S (flt_min): New object.
        (MO): New macro.
        (__atanf): For results with small absolute value, force underflow
        exception and remove excess range and precision from return value.
        * sysdeps/ieee754/dbl-64/e_atan2.c: Include <float.h> and
        <math.h>.
        (__ieee754_atan2): Force underflow exception for results with
        small absolute value.
        * sysdeps/ieee754/dbl-64/s_atan.c: Include <float.h> and
        <math_private.h>.
        (atan): Force underflow exception for results with small absolute
        value.
        * sysdeps/ieee754/flt-32/s_atanf.c: Include <float.h>.
        (__atanf): Force underflow exception for results with small
        absolute value.
        * sysdeps/ieee754/ldbl-128/s_atanl.c: Include <float.h> and
        <math.h>.
        (__atanl): Force underflow exception for results with small
        absolute value.
        * sysdeps/ieee754/ldbl-128ibm/s_atanl.c: Include <float.h>.
        (__atanl): Force underflow exception for results with small
        absolute value.
        * sysdeps/x86/fpu/bits/mathinline.h
        [!__SSE2_MATH__ && !__x86_64__ && __LIBC_INTERNAL_MATH_INLINES]
        (__ieee754_atan2): Only define inline for long double.
        * sysdeps/x86_64/fpu/multiarch/e_atan2.c
        [HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Include <math.h>.
        * math/auto-libm-test-in: Do not mark underflow exceptions as
        possibly missing for bug 15319.  Add more tests of atan2.
        * math/auto-libm-test-out: Regenerated.
        * math/libm-test.inc (casin_test_data): Do not mark underflow
        exceptions as possibly missing for bug 15319.
        (casinh_test_data): Likewise.
        * sysdeps/i386/fpu/libm-test-ulps: Update.

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

Summary of changes:
 ChangeLog                              |   52 +
 NEWS                                   |    4 +-
 math/auto-libm-test-in                 |   36 +-
 math/auto-libm-test-out                | 2434 ++++++++++++++++++++------------
 math/libm-test.inc                     |   90 +-
 sysdeps/i386/fpu/e_atan2.S             |   35 +-
 sysdeps/i386/fpu/e_atan2f.S            |   35 +-
 sysdeps/i386/fpu/libm-test-ulps        |   24 +-
 sysdeps/i386/fpu/s_atan.S              |   33 +-
 sysdeps/i386/fpu/s_atanf.S             |   33 +-
 sysdeps/ieee754/dbl-64/e_atan2.c       |   14 +-
 sysdeps/ieee754/dbl-64/s_atan.c        |   11 +-
 sysdeps/ieee754/flt-32/s_atanf.c       |    6 +
 sysdeps/ieee754/ldbl-128/s_atanl.c     |    7 +
 sysdeps/ieee754/ldbl-128ibm/s_atanl.c  |    6 +
 sysdeps/x86/fpu/bits/mathinline.h      |   12 +-
 sysdeps/x86_64/fpu/multiarch/e_atan2.c |    1 +
 17 files changed, 1840 insertions(+), 993 deletions(-)

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