[Bug math/21094] cosf(1.57079697) has 3 ulp error on targets where the generic c code is used

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https://sourceware.org/bugzilla/show_bug.cgi?id=21094

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=e4e52ff059f46472145433d2bd003d5383f89e82

commit e4e52ff059f46472145433d2bd003d5383f89e82
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Wed Mar 15 22:00:54 2017 +0000

    Improve float range reduction accuracy near pi/2 (bug 21094).

    Bug 21094 reports 3ulp errors of cosf and tanf for certain arguments
    near pi/2 arising from the use of an insufficiently accurate range
    reduction.  (To be clear, this is a quality-of-implementation issue
    relating to the apparent intent of those particular cosf and tanf
    implementations; 3ulp is within the general glibc accuracy goals, so
    not inherently a bug.)

    This patch fixes that error by making a wider range of cases use the
    existing more accurate range reduction for arguments close to pi/2.
    The wider range of values is still narrow enough for the "z -=
    pio2_2;" in the more accurate case to be exact, as the code expects.

    Tested for x86_64, x86 and mips64; no ulps updates needed (but at
    least on mips64, the larger ulps were seen if the tests were added
    without the substantive fix).

        [BZ #21094]
        * sysdeps/ieee754/flt-32/e_rem_pio2f.c (__ieee754_rem_pio2f): Use
        24+24+24-bit pi for wider range of values around pi/2.
        * math/auto-libm-test-in: Add more tests of cos and tan.
        * math/auto-libm-test-out-cos: Regenerated.
        * math/auto-libm-test-out-tan: Likewise.

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

Summary of changes:
 ChangeLog                            |    9 +
 math/auto-libm-test-in               |    4 +
 math/auto-libm-test-out-cos          |  290 ++++++++++++++++++++++++++++++++++
 math/auto-libm-test-out-tan          |  290 ++++++++++++++++++++++++++++++++++
 sysdeps/ieee754/flt-32/e_rem_pio2f.c |    4 +-
 5 files changed, 595 insertions(+), 2 deletions(-)

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