[Bug math/19016] clog, clog10 inaccuracy

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https://sourceware.org/bugzilla/show_bug.cgi?id=19016

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https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=a5721ebc68cc8b761b0ffdf6dcae52723369e071

commit a5721ebc68cc8b761b0ffdf6dcae52723369e071
Author: Joseph Myers <joseph@codesourcery.com>
Date:   Mon Sep 28 22:11:22 2015 +0000

    Fix clog, clog10 inaccuracy (bug 19016).

    For arguments with X^2 + Y^2 close to 1, clog and clog10 avoid large
    errors from log(hypot) by computing X^2 + Y^2 - 1 in a way that avoids
    cancellation error and then using log1p.

    However, the thresholds for using that approach still result in log
    being used on argument as large as sqrt(13/16) > 0.9, leading to
    significant errors, in some cases above the 9ulp maximum allowed in
    glibc libm.  This patch arranges for the approach using log1p to be
    used in any cases where |X|, |Y| < 1 and X^2 + Y^2 >= 0.5 (with the
    existing allowance for cases where one of X and Y is very small),
    adjusting the __x2y2m1 functions to work with the wider range of
    inputs.  This way, log only gets used on arguments below sqrt(1/2) (or
    substantially above 1), where the error involved is much less.

    Tested for x86_64, x86, mips64 and powerpc.  For the ulps regeneration
    I removed the existing clog and clog10 ulps before regenerating to
    allow any reduced ulps to appear.  Tests added include those found by
    random test generation to produce large ulps either before or after
    the patch, and some found by trying inputs close to the (0.75, 0.5)
    threshold where the potential errors from using log are largest.

        [BZ #19016]
        * sysdeps/generic/math_private.h (__x2y2m1f): Update comment to
        allow more cases with X^2 + Y^2 >= 0.5.
        * sysdeps/ieee754/dbl-64/x2y2m1.c (__x2y2m1): Likewise.  Add -1 as
        normal element in sum instead of special-casing based on values of
        arguments.
        * sysdeps/ieee754/dbl-64/x2y2m1f.c (__x2y2m1f): Update comment.
        * sysdeps/ieee754/ldbl-128/x2y2m1l.c (__x2y2m1l): Likewise.  Add
        -1 as normal element in sum instead of special-casing based on
        values of arguments.
        * sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c (__x2y2m1l): Likewise.
        * sysdeps/ieee754/ldbl-96/x2y2m1.c [FLT_EVAL_METHOD != 0]
        (__x2y2m1): Update comment.
        * sysdeps/ieee754/ldbl-96/x2y2m1l.c (__x2y2m1l): Likewise.  Add -1
        as normal element in sum instead of special-casing based on values
        of arguments.
        * math/s_clog.c (__clog): Handle more cases using log1p without
        hypot.
        * math/s_clog10.c (__clog10): Likewise.
        * math/s_clog10f.c (__clog10f): Likewise.
        * math/s_clog10l.c (__clog10l): Likewise.
        * math/s_clogf.c (__clogf): Likewise.
        * math/s_clogl.c (__clogl): Likewise.
        * math/auto-libm-test-in: Add more tests of clog and clog10.
        * math/auto-libm-test-out: Regenerated.
        * sysdeps/i386/fpu/libm-test-ulps: Update.
        * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

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

Summary of changes:
 ChangeLog                             |   30 +
 NEWS                                  |    3 +-
 math/auto-libm-test-in                |   90 +
 math/auto-libm-test-out               | 6488 +++++++++++++++++++++++++++++++++
 math/s_clog.c                         |    7 +-
 math/s_clog10.c                       |    7 +-
 math/s_clog10f.c                      |    7 +-
 math/s_clog10l.c                      |    7 +-
 math/s_clogf.c                        |    7 +-
 math/s_clogl.c                        |    7 +-
 sysdeps/generic/math_private.h        |    4 +-
 sysdeps/i386/fpu/libm-test-ulps       |   80 +-
 sysdeps/ieee754/dbl-64/x2y2m1.c       |   22 +-
 sysdeps/ieee754/dbl-64/x2y2m1f.c      |    4 +-
 sysdeps/ieee754/ldbl-128/x2y2m1l.c    |   22 +-
 sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c |   24 +-
 sysdeps/ieee754/ldbl-96/x2y2m1.c      |    4 +-
 sysdeps/ieee754/ldbl-96/x2y2m1l.c     |   22 +-
 sysdeps/x86_64/fpu/libm-test-ulps     |   80 +-
 19 files changed, 6759 insertions(+), 156 deletions(-)

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