[Bug math/16516] spurious underflow exception from erff

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https://sourceware.org/bugzilla/show_bug.cgi?id=16516

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=0bf061d3e37e0f72c2378cbded67c58df4f58a4b

commit 0bf061d3e37e0f72c2378cbded67c58df4f58a4b
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Wed May 14 12:34:03 2014 +0000

    Fix erf underflow handling near 0 (bug 16516).

    Bug 16516 reports spurious underflows from erf (for all floating-point
    types), when the result is close to underflowing but does not actually
    underflow.

    erf (x) is about (2/sqrt(pi))*x for x close to 0, so there are
    subnormal arguments for which it does not underflow.  The various
    implementations do (x + efx*x) (for efx = 2/sqrt(pi) - 1), for greater
    accuracy than if just using a single multiplication by an
    approximation to 2/sqrt(pi) (effectively, this way there are a few
    more bits in the approximation to 2/sqrt(pi)).  This can introduce
    underflows when efx*x underflows even though the final result does
    not, so a scaled calculation with 8*efx is done in these cases - but 8
    is not a big enough scale factor to avoid all such underflows.  16 is
    (any underflows with a scale factor of 16 would only occur when the
    final result underflows), so this patch changes the code to use that
    factor.  Rather than recomputing all the values of the efx8 variable,
    it is removed, leaving it to the compiler's constant folding to
    compute 16*efx.  As such scaling can also lose underflows when the
    final scaling down happens to be exact, appropriate checks are added
    to ensure underflow exceptions occur when required in such cases.

    Tested x86_64 and x86; no ulps updates needed.  Also spot-checked for
    powerpc32 and mips64 to verify the changes to the ldbl-128ibm and
    ldbl-128 implementations.

        [BZ #16516]
        * sysdeps/ieee754/dbl-64/s_erf.c (efx8): Remove variable.
        (__erf): Scale by 16 instead of 8 in potentially underflowing
        case.  Ensure exception if result actually underflows.
        * sysdeps/ieee754/flt-32/s_erff.c (efx8): Remove variable.
        (__erff): Scale by 16 instead of 8 in potentially underflowing
        case.  Ensure exception if result actually underflows.
        * sysdeps/ieee754/ldbl-128/s_erfl.c: Include <float.h>.
        (efx8): Remove variable.
        (__erfl): Scale by 16 instead of 8 in potentially underflowing
        case.  Ensure exception if result actually underflows.
        * sysdeps/ieee754/ldbl-128ibm/s_erfl.c: Include <float.h>.
        (efx8): Remove variable.
        (__erfl): Scale by 16 instead of 8 in potentially underflowing
        case.  Ensure exception if result actually underflows.
        * sysdeps/ieee754/ldbl-96/s_erfl.c: Include <float.h>.
        (efx8): Remove variable.
        (__erfl): Scale by 16 instead of 8 in potentially underflowing
        case.  Ensure exception if result actually underflows.
        * math/auto-libm-test-in: Add more tests of erf.
        * math/auto-libm-test-out: Regenerated.

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

Summary of changes:
 ChangeLog                            |   24 ++++
 NEWS                                 |   13 +-
 math/auto-libm-test-in               |    4 +
 math/auto-libm-test-out              |  200 ++++++++++++++++++++++++++++++++++
 sysdeps/ieee754/dbl-64/s_erf.c       |   12 ++-
 sysdeps/ieee754/flt-32/s_erff.c      |   13 ++-
 sysdeps/ieee754/ldbl-128/s_erfl.c    |   16 ++-
 sysdeps/ieee754/ldbl-128ibm/s_erfl.c |   16 ++-
 sysdeps/ieee754/ldbl-96/s_erfl.c     |   14 ++-
 9 files changed, 289 insertions(+), 23 deletions(-)

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