[Bug math/18613] New: tgamma inaccurate in non-default rounding modes

[Bug math/18613] New: tgamma inaccurate in non-default rounding modes

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=18613

            Bug ID: 18613
           Summary: tgamma inaccurate in non-default rounding modes
           Product: glibc
           Version: 2.21
            Status: NEW
          Severity: normal
          Priority: P2
         Component: math
          Assignee: unassigned at sourceware dot org
          Reporter: jsm28 at gcc dot gnu.org
  Target Milestone: ---

In non-default rounding modes, tgamma can be slightly less accurate than
permitted by glibc's accuracy goals, e.g. for double on x86_64:

Failure: Test: tgamma_towardzero (-0x6.fe4638p+0)
Result:
 is:         -2.98383122695617016006e-02  -0x1.e8def3d7660a50000000p-6
 should be:  -2.98383122695616634367e-02  -0x1.e8def3d76609a0000000p-6
 difference:  3.81639164714897560770e-17   0x1.60000000000000000000p-55
 ulp       :  11.0000
 max.ulp   :  0.0000

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[Bug math/18613] tgamma inaccurate in non-default rounding modes

[cvs-commit at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=18613

--- Comment #1 from cvs-commit at gcc dot gnu.org <cvs-commit at gcc dot gnu.org> ---
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- Log -----------------------------------------------------------------
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=e02920bc029019443326eecaa7b267b78ff2892e

commit e02920bc029019443326eecaa7b267b78ff2892e
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Mon Jun 29 23:29:35 2015 +0000

    Improve tgamma accuracy (bug 18613).

    In non-default rounding modes, tgamma can be slightly less accurate
    than permitted by glibc's accuracy goals.

    Part of the problem is error accumulation, addressed in this patch by
    setting round-to-nearest for internal computations.  However, there
    was also a bug in the code dealing with computing pow (x + n, x + n)
    where x + n is not exactly representable, providing another source of
    error even in round-to-nearest mode; it was necessary to address both
    bugs to get errors for all testcases within glibc's accuracy goals.
    Given this second fix, accuracy in round-to-nearest mode is also
    improved (hence regeneration of ulps for tgamma should be from scratch
    - truncate libm-test-ulps or at least remove existing tgamma entries -
    so that the expected ulps can be reduced).

    Some additional complications also arose.  Certain tgamma tests should
    strictly, according to IEEE semantics, overflow or not depending on
    the rounding mode; this is beyond the scope of glibc's accuracy goals
    for any function without exactly-determined results, but
    gen-auto-libm-tests doesn't handle being lax there as it does for
    underflow.  (libm-test.inc also doesn't handle being lax about whether
    the result in cases very close to the overflow threshold is infinity
    or a finite value close to overflow, but that doesn't cause problems
    in this case though I've seen it cause problems with random test
    generation for some functions.)  Thus, spurious-overflow markings,
    with a comment, are added to auto-libm-test-in (no bug in Bugzilla
    because the issue is with the testsuite, not a user-visible bug in
    glibc).  And on x86, after the patch I saw ERANGE issues as previously
    reported by Carlos (see my commentary in
    <https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>), which
    needed addressing by ensuring excess range and precision were
    eliminated at various points if FLT_EVAL_METHOD != 0.

    I also noticed and fixed a cosmetic issue where 1.0f was used in long
    double functions and should have been 1.0L.

    This completes the move of all functions to testing in all rounding
    modes with ALL_RM_TEST, so gen-libm-have-vector-test.sh is updated to
    remove the workaround for some functions not using ALL_RM_TEST.

    Tested for x86_64, x86, mips64 and powerpc.

        [BZ #18613]
        * sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Take log of
        X_ADJ not X when adjusting exponent.
        (__ieee754_gamma_r): Do intermediate computations in
        round-to-nearest then adjust overflowing and underflowing results
        as needed.
        * sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Take log
        of X_ADJ not X when adjusting exponent.
        (__ieee754_gammaf_r): Do intermediate computations in
        round-to-nearest then adjust overflowing and underflowing results
        as needed.
        * sysdeps/ieee754/ldbl-128/e_gammal_r.c (gammal_positive): Take
        log of X_ADJ not X when adjusting exponent.
        (__ieee754_gammal_r): Do intermediate computations in
        round-to-nearest then adjust overflowing and underflowing results
        as needed.  Use 1.0L not 1.0f as numerator of division.
        * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (gammal_positive): Take
        log of X_ADJ not X when adjusting exponent.
        (__ieee754_gammal_r): Do intermediate computations in
        round-to-nearest then adjust overflowing and underflowing results
        as needed.  Use 1.0L not 1.0f as numerator of division.
        * sysdeps/ieee754/ldbl-96/e_gammal_r.c (gammal_positive): Take log
        of X_ADJ not X when adjusting exponent.
        (__ieee754_gammal_r): Do intermediate computations in
        round-to-nearest then adjust overflowing and underflowing results
        as needed.  Use 1.0L not 1.0f as numerator of division.
        * math/libm-test.inc (tgamma_test_data): Remove one test.  Moved
        to auto-libm-test-in.
        (tgamma_test): Use ALL_RM_TEST.
        * math/auto-libm-test-in: Add one test of tgamma.  Mark some other
        tests of tgamma with spurious-overflow.
        * math/auto-libm-test-out: Regenerated.
        * math/gen-libm-have-vector-test.sh: Do not check for START.
        * sysdeps/i386/fpu/libm-test-ulps: Update.
        * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

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

Summary of changes:
 ChangeLog                                |   36 ++++
 NEWS                                     |    2 +-
 math/auto-libm-test-in                   |   10 +-
 math/auto-libm-test-out                  |  263 +++++++++++++++++++-----------
 math/gen-libm-have-vector-test.sh        |    8 -
 math/libm-test.inc                       |    5 +-
 sysdeps/i386/fpu/libm-test-ulps          |   36 ++++-
 sysdeps/ieee754/dbl-64/e_gamma_r.c       |   87 +++++++---
 sysdeps/ieee754/flt-32/e_gammaf_r.c      |   88 +++++++---
 sysdeps/ieee754/ldbl-128/e_gammal_r.c    |   74 ++++++---
 sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c |   74 ++++++---
 sysdeps/ieee754/ldbl-96/e_gammal_r.c     |   74 ++++++---
 sysdeps/x86_64/fpu/libm-test-ulps        |   32 +++-
 13 files changed, 540 insertions(+), 249 deletions(-)

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[Bug math/18613] tgamma inaccurate in non-default rounding modes

[jsm28 at gcc dot gnu.org]

https://sourceware.org/bugzilla/show_bug.cgi?id=18613

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 2.22.

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