[Bug math/18371] csqrt spurious underflows

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https://sourceware.org/bugzilla/show_bug.cgi?id=18371

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=718d34a309493f8697ff9a8fefcbacbba12a2ccd

commit 718d34a309493f8697ff9a8fefcbacbba12a2ccd
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Tue Jun 23 16:01:54 2015 +0000

    Fix csqrt spurious underflows (bug 18371).

    The csqrt implementations in glibc can cause spurious underflows in
    some cases as a side-effect of the scaling for large arguments (when
    underflow is correct for the square root of the argument that was
    scaled down to avoid overflow, but not for the original argument).
    This patch arranges to avoid the underflowing intermediate computation
    (eliminating a multiplication in 0.5 in the problem cases where a
    subsequent scaling by 2 would follow).

    Tested for x86_64 and x86 and ulps updated accordingly (only needed
    for x86).

        [BZ #18371]
        * math/s_csqrt.c (__csqrt): Avoid multiplication by 0.5 where
        intermediate but not final result might underflow.
        * math/s_csqrtf.c (__csqrtf): Likewise.
        * math/s_csqrtl.c (__csqrtl): Likewise.
        * math/auto-libm-test-in: Add more tests of csqrt.
        * math/auto-libm-test-out: Regenerated.
        * sysdeps/i386/fpu/libm-test-ulps: Update.

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

Summary of changes:
 ChangeLog                       |    9 +
 NEWS                            |   10 +-
 math/auto-libm-test-in          |    7 +
 math/auto-libm-test-out         |  766 +++++++++++++++++++++++++++++++++++++++
 math/s_csqrt.c                  |   20 +-
 math/s_csqrtf.c                 |   20 +-
 math/s_csqrtl.c                 |   20 +-
 sysdeps/i386/fpu/libm-test-ulps |    2 +
 8 files changed, 843 insertions(+), 11 deletions(-)

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