[Bug math/17061] New: [ldbl-128/ldbl-128ibm] coshl inaccurate near 0

[Bug math/17061] New: [ldbl-128/ldbl-128ibm] coshl inaccurate near 0

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=17061

            Bug ID: 17061
           Summary: [ldbl-128/ldbl-128ibm] coshl inaccurate near 0
           Product: glibc
           Version: 2.19
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
          Assignee: unassigned at sourceware dot org
          Reporter: jsm28 at gcc dot gnu.org

The ldbl-128 and ldbl-128ibm implementations of coshl have a threshold for
small arguments for which the result (to nearest) is 1.  However, in those
cases they return 1 + expm1(abs(x)) rather than 1, and while the threshold is
small enough for cosh(x) (1 + x^2/2 + ...) to be 1, it's not small enough for 1
+ abs(x) to be 1, resulting in large errors.  E.g., for ldbl-128:

Failure: Test: cosh (0x1p-72)
Result:
 is:          1.00000000000000000000e+00   0x1.00000000000000000100p+0
 should be:   1.00000000000000000000e+00   0x1.00000000000000000000p+0
 difference:  2.11758236813575084767e-22   0x1.00000000000000000000p-72
 ulp       :  1099511627776.0000
 max.ulp   :  1.0000

and for ldbl-128ibm:

Failure: Test: cosh (0x1p-56)
Result:
 is:          1.00000000000000001388e+00   0x1.00000000000001000000p+0
 should be:   1.00000000000000000000e+00   0x1.00000000000000000000p+0
 difference:  1.38777878078144567553e-17   0x1.00000000000000000000p-56
 ulp       :  562949953421312.0000
 max.ulp   :  3.0000

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[Bug math/17061] [ldbl-128/ldbl-128ibm] coshl inaccurate near 0

[fweimer at redhat dot com]

https://sourceware.org/bugzilla/show_bug.cgi?id=17061

Florian Weimer <fweimer at redhat dot com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
              Flags|                            |security-

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[Bug math/17061] [ldbl-128/ldbl-128ibm] coshl inaccurate near 0

[cvs-commit at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=17061

--- Comment #1 from cvs-commit at gcc dot gnu.org <cvs-commit at gcc dot gnu.org> ---
This is an automated email from the git hooks/post-receive script. It was
generated because a ref change was pushed to the repository containing
the project "GNU C Library master sources".

The branch, master has been updated
       via  4648909d56c1e9063017bcddd3271dffadef7cb5 (commit)
      from  46a3d3c7d60db15ea65470800bcba695f55ce6f6 (commit)

Those revisions listed above that are new to this repository have
not appeared on any other notification email; so we list those
revisions in full, below.

- Log -----------------------------------------------------------------
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=4648909d56c1e9063017bcddd3271dffadef7cb5

commit 4648909d56c1e9063017bcddd3271dffadef7cb5
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Mon Jun 23 20:20:10 2014 +0000

    Fix cosh spurious underflows from expm1 (bug 16354), inaccurate results
near 0 (bug 17061).

    This patch fixes bug 16354, spurious underflows from cosh when a tiny
    argument is passed to expm1 and expm1 correctly underflows although
    the final result of cosh should be 1.  As noted in that bug, some
    cases are latent because of expm1 implementations not raising
    underflow (bug 16353), but all the implementations are fixed
    similarly.  They already contained checks for tiny arguments, but the
    checks were too late to avoid underflow from expm1 (although they
    would avoid underflow from subsequent squaring of the result of
    expm1); they are moved before the expm1 calls.

    The thresholds used for considering arguments tiny are not
    particularly consistent in how they relate to the precision of the
    floating-point format in question.  They are, however, all sufficient
    to ensure that the round-to-nearest result of cosh is indeed 1 below
    the threshold (although sometimes they are smaller than necessary).
    But the previous logic did not return 1, but the previously computed 1
    + expm1(abs(x)) value.  And the thresholds in the ldbl-128 and
    ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code
    instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for
    that value to be 1.  So by moving the test for tiny arguments, and
    consequently returning 1 directly now the expm1 value hasn't been
    computed by that point, this patch also fixes bug 17061, the (large
    number of ulps) inaccuracy for small arguments in those
    implementations.  Tests for that bug are duly added.

    Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
    mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes.

        [BZ #16354]
        [BZ #17061]
        * sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for
        small arguments before calling __expm1.
        * sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for
        small arguments before calling __expm1f.
        * sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for
        small arguments before calling __expm1l.
        * sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl):
        Likewise.
        * sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise.
        * math/auto-libm-test-in: Add more cosh tests.  Do not allow
        spurious underflow for some cosh tests.
        * math/auto-libm-test-out: Regenerated.
        * sysdeps/i386/fpu/libm-test-ulps: Update.

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

Summary of changes:
 ChangeLog                             |   16 +
 NEWS                                  |   20 +-
 math/auto-libm-test-in                |   13 +-
 math/auto-libm-test-out               |  732 +++++++++++++++++++--------------
 sysdeps/i386/fpu/libm-test-ulps       |    1 +
 sysdeps/ieee754/dbl-64/e_cosh.c       |    4 +-
 sysdeps/ieee754/flt-32/e_coshf.c      |    2 +-
 sysdeps/ieee754/ldbl-128/e_coshl.c    |    4 +-
 sysdeps/ieee754/ldbl-128ibm/e_coshl.c |    2 +-
 sysdeps/ieee754/ldbl-96/e_coshl.c     |    2 +-
 10 files changed, 458 insertions(+), 338 deletions(-)

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[Bug math/17061] [ldbl-128/ldbl-128ibm] coshl inaccurate near 0

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=17061

Joseph Myers <jsm28 at gcc dot gnu.org> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
             Status|NEW                         |RESOLVED
         Resolution|---                         |FIXED

--- Comment #2 from Joseph Myers <jsm28 at gcc dot gnu.org> ---
Fixed for 2.20.

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