[Bug math/18219] exp2, exp2f spurious underflows

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https://sourceware.org/bugzilla/show_bug.cgi?id=18219

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=b59549574efeeecf124de05c9183c120eaaa56f0

commit b59549574efeeecf124de05c9183c120eaaa56f0
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Tue Jun 23 14:35:18 2015 +0000

    Fix exp2, exp2f spurious underflows (bug 18219).

    The dbl-64 and flt-32 implementations of exp2 functions produce
    spurious underflow exceptions.  The underlying reason is the same in
    both cases: the computation works as (2^a - 1)*2^b + 2^b for suitably
    chosen a and b, where a has small magnitude so 2^a - 1 can be computed
    with a low-degree polynomial approximation, and (2^a - 1)*2^b can
    underflow even when the final result does not.  This patch fixes this
    by adjusting the threshold for when scaling is used to avoid
    intermediate underflow so it works for any possible value of a where
    the final result would not underflow.

    Tested for x86_64 and x86.

        [BZ #18219]
        * sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Reduce
        threshold on absolute value of exponent for which scaling is used.
        * sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise.
        * math/auto-libm-test-in: Add more tests of exp2.
        * math/auto-libm-test-out: Regenerated.

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

Summary of changes:
 ChangeLog                        |    9 ++
 NEWS                             |   12 ++--
 math/auto-libm-test-in           |    7 ++
 math/auto-libm-test-out          |  175 ++++++++++++++++++++++++++++++++++++++
 sysdeps/ieee754/dbl-64/e_exp2.c  |    4 +-
 sysdeps/ieee754/flt-32/e_exp2f.c |    4 +-
 6 files changed, 203 insertions(+), 8 deletions(-)

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