[Bug math/18217] erfcf spurious underflows

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https://sourceware.org/bugzilla/show_bug.cgi?id=18217

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=fbc68f03b0e56db6a07d789fd403eb79d726fe96

commit fbc68f03b0e56db6a07d789fd403eb79d726fe96
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Fri May 15 00:16:10 2015 +0000

    Fix erfcf spurious underflows (bug 18217).

    The flt-32 implementation of erfcf produces spurious underflow
    exceptions for some arguments close to 0, because of calculations
    squaring the argument and then multiplying by small constants.  This
    patch fixes this by adjusting the threshold for arguments for which
    the result is so close to 1 that 1 - x will give the right result from
    2**-56 to 2**-26.  (If 1 - x * 2/sqrt(pi) were used, the errors would be
    on the order of x^3 and a much larger threshold could be used.)

    Tested for x86_64 and x86.

        [BZ #18217]
        * sysdeps/ieee754/flt-32/s_erff.c (__erfcf): Use 2**-26 not 2**-56
        as threshold for returning 1 - x.
        * math/auto-libm-test-in: Add more tests of erfc.
        * math/auto-libm-test-out: Regenerated.

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

Summary of changes:
 ChangeLog                       |    8 ++++++
 NEWS                            |    4 +-
 math/auto-libm-test-in          |    2 +
 math/auto-libm-test-out         |   50 +++++++++++++++++++++++++++++++++++++++
 sysdeps/ieee754/flt-32/s_erff.c |    2 +-
 5 files changed, 63 insertions(+), 3 deletions(-)

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