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Author SHA1 Message Date
Paul Eggert
5a82c74822 Prefer https to http for gnu.org and fsf.org URLs 
Also, change sources.redhat.com to sourceware.org.
This patch was automatically generated by running the following shell
script, which uses GNU sed, and which avoids modifying files imported
from upstream:

sed -ri '
  s,(http|ftp)(://(.*\.)?(gnu|fsf|sourceware)\.org($|[^.]|\.[^a-z])),https\2,g
  s,(http|ftp)(://(.*\.)?)sources\.redhat\.com($|[^.]|\.[^a-z]),https\2sourceware.org\4,g
' \
  $(find $(git ls-files) -prune -type f \
      ! -name '*.po' \
      ! -name 'ChangeLog*' \
      ! -path COPYING ! -path COPYING.LIB \
      ! -path manual/fdl-1.3.texi ! -path manual/lgpl-2.1.texi \
      ! -path manual/texinfo.tex ! -path scripts/config.guess \
      ! -path scripts/config.sub ! -path scripts/install-sh \
      ! -path scripts/mkinstalldirs ! -path scripts/move-if-change \
      ! -path INSTALL ! -path  locale/programs/charmap-kw.h \
      ! -path po/libc.pot ! -path sysdeps/gnu/errlist.c \
      ! '(' -name configure \
            -execdir test -f configure.ac -o -f configure.in ';' ')' \
      ! '(' -name preconfigure \
            -execdir test -f preconfigure.ac ';' ')' \
      -print)

and then by running 'make dist-prepare' to regenerate files built
from the altered files, and then executing the following to cleanup:

  chmod a+x sysdeps/unix/sysv/linux/riscv/configure
  # Omit irrelevant whitespace and comment-only changes,
  # perhaps from a slightly-different Autoconf version.
  git checkout -f \
    sysdeps/csky/configure \
    sysdeps/hppa/configure \
    sysdeps/riscv/configure \
    sysdeps/unix/sysv/linux/csky/configure
  # Omit changes that caused a pre-commit check to fail like this:
  # remote: *** error: sysdeps/powerpc/powerpc64/ppc-mcount.S: trailing lines
  git checkout -f \
    sysdeps/powerpc/powerpc64/ppc-mcount.S \
    sysdeps/unix/sysv/linux/s390/s390-64/syscall.S
  # Omit change that caused a pre-commit check to fail like this:
  # remote: *** error: sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S: last line does not end in newline
  git checkout -f sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S
 2019-09-07 02:43:31 -07:00
Joseph Myers
04277e02d7 Update copyright dates with scripts/update-copyrights. 
* All files with FSF copyright notices: Update copyright dates
	using scripts/update-copyrights.
	* locale/programs/charmap-kw.h: Regenerated.
	* locale/programs/locfile-kw.h: Likewise.
 2019-01-01 00:11:28 +00:00
Joseph Myers
e44acb2063 Use floor functions not __floor functions in glibc libm. 
Similar to the changes that were made to call sqrt functions directly
in glibc, instead of __ieee754_sqrt variants, so that the compiler
could inline them automatically without needing special inline
definitions in lots of math_private.h headers, this patch makes libm
code call floor functions directly instead of __floor variants,
removing the inlines / macros for x86_64 (SSE4.1) and powerpc
(POWER5).

The redirection used to ensure that __ieee754_sqrt does still get
called when the compiler doesn't inline a built-in function expansion
is refactored so it can be applied to other functions; the refactoring
is arranged so it's not limited to unary functions either (it would be
reasonable to use this mechanism for copysign - removing the inline in
math_private_calls.h but also eliminating unnecessary local PLT entry
use in the cases (powerpc soft-float and e500v1, for IBM long double)
where copysign calls don't get inlined).

The point of this change is that more architectures can get floor
calls inlined where they weren't previously (AArch64, for example),
without needing special inline definitions in their math_private.h,
and existing such definitions in math_private.h headers can be
removed.

Note that it's possible that in some cases an inline may be used where
an IFUNC call was previously used - this is the case on x86_64, for
example.  I think the direct calls to floor are still appropriate; if
there's any significant performance cost from inline SSE2 floor
instead of an IFUNC call ending up with SSE4.1 floor, that indicates
that either the function should be doing something else that's faster
than using floor at all, or it should itself have IFUNC variants, or
that the compiler choice of inlining for generic tuning should change
to allow for the possibility that, by not inlining, an SSE4.1 IFUNC
might be called at runtime - but not that glibc should avoid calling
floor internally.  (After all, all the same considerations would apply
to any user program calling floor, where it might either be inlined or
left as an out-of-line call allowing for a possible IFUNC.)

Tested for x86_64, and with build-many-glibcs.py.

	* include/math.h [!_ISOMAC && !(__FINITE_MATH_ONLY__ &&
	__FINITE_MATH_ONLY__ > 0) && !NO_MATH_REDIRECT] (MATH_REDIRECT):
	New macro.
	[!_ISOMAC && !(__FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0)
	&& !NO_MATH_REDIRECT] (MATH_REDIRECT_LDBL): Likewise.
	[!_ISOMAC && !(__FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0)
	&& !NO_MATH_REDIRECT] (MATH_REDIRECT_F128): Likewise.
	[!_ISOMAC && !(__FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0)
	&& !NO_MATH_REDIRECT] (MATH_REDIRECT_UNARY_ARGS): Likewise.
	[!_ISOMAC && !(__FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0)
	&& !NO_MATH_REDIRECT] (sqrt): Redirect using MATH_REDIRECT.
	[!_ISOMAC && !(__FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0)
	&& !NO_MATH_REDIRECT] (floor): Likewise.
	* sysdeps/aarch64/fpu/s_floor.c: Define NO_MATH_REDIRECT before
	header inclusion.
	* sysdeps/aarch64/fpu/s_floorf.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_floor.c: Likewise.
	* sysdeps/ieee754/dbl-64/wordsize-64/s_floor.c: Likewise.
	* sysdeps/ieee754/float128/s_floorf128.c: Likewise.
	* sysdeps/ieee754/flt-32/s_floorf.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_floorl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_floorl.c: Likewise.
	* sysdeps/m68k/m680x0/fpu/s_floor_template.c: Likewise.
	* sysdeps/powerpc/powerpc32/power4/fpu/multiarch/s_floor.c: Likewise.
	* sysdeps/powerpc/powerpc32/power4/fpu/multiarch/s_floorf.c: Likewise.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/s_floor.c: Likewise.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/s_floorf.c: Likewise.
	* sysdeps/riscv/rv64/rvd/s_floor.c: Likewise.
	* sysdeps/riscv/rvf/s_floorf.c: Likewise.
	* sysdeps/sparc/sparc64/fpu/multiarch/s_floor.c: Likewise.
	* sysdeps/sparc/sparc64/fpu/multiarch/s_floorf.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/s_floor.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/s_floorf.c: Likewise.
	* sysdeps/powerpc/fpu/math_private.h [_ARCH_PWR5X] (__floor):
	Remove macro.
	[_ARCH_PWR5X] (__floorf): Likewise.
	* sysdeps/x86_64/fpu/math_private.h [__SSE4_1__] (__floor): Remove
	inline function.
	[__SSE4_1__] (__floorf): Likewise.
	* math/w_lgamma_main.c (LGFUNC (__lgamma)): Use floor functions
	instead of __floor variants.
	* math/w_lgamma_r_compat.c (__lgamma_r): Likewise.
	* math/w_lgammaf_main.c (LGFUNC (__lgammaf)): Likewise.
	* math/w_lgammaf_r_compat.c (__lgammaf_r): Likewise.
	* math/w_lgammal_main.c (LGFUNC (__lgammal)): Likewise.
	* math/w_lgammal_r_compat.c (__lgammal_r): Likewise.
	* math/w_tgamma_compat.c (__tgamma): Likewise.
	* math/w_tgamma_template.c (M_DECL_FUNC (__tgamma)): Likewise.
	* math/w_tgammaf_compat.c (__tgammaf): Likewise.
	* math/w_tgammal_compat.c (__tgammal): Likewise.
	* sysdeps/ieee754/dbl-64/e_lgamma_r.c (sin_pi): Likewise.
	* sysdeps/ieee754/dbl-64/k_rem_pio2.c (__kernel_rem_pio2):
	Likewise.
	* sysdeps/ieee754/dbl-64/lgamma_neg.c (__lgamma_neg): Likewise.
	* sysdeps/ieee754/flt-32/e_lgammaf_r.c (sin_pif): Likewise.
	* sysdeps/ieee754/flt-32/lgamma_negf.c (__lgamma_negf): Likewise.
	* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
	Likewise.
	* sysdeps/ieee754/ldbl-128/e_powl.c (__ieee754_powl): Likewise.
	* sysdeps/ieee754/ldbl-128/lgamma_negl.c (__lgamma_negl):
	Likewise.
	* sysdeps/ieee754/ldbl-128/s_expm1l.c (__expm1l): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c (__ieee754_lgammal_r):
	Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c (__lgamma_negl):
	Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_expm1l.c (__expm1l): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_truncl.c (__truncl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_lgammal_r.c (sin_pi): Likewise.
	* sysdeps/ieee754/ldbl-96/lgamma_negl.c (__lgamma_negl): Likewise.
	* sysdeps/powerpc/power5+/fpu/s_modf.c (__modf): Likewise.
	* sysdeps/powerpc/power5+/fpu/s_modff.c (__modff): Likewise.
 2018-09-14 13:09:01 +00:00
Joseph Myers
70e2ba332f Do not include fenv_private.h in math_private.h. 
Continuing the clean-up related to the catch-all math_private.h
header, this patch stops math_private.h from including fenv_private.h.
Instead, fenv_private.h is included directly from those users of
math_private.h that also used interfaces from fenv_private.h.  No
attempt is made to remove unused includes of math_private.h, but that
is a natural followup.

(However, since math_private.h sometimes defines optimized versions of
math.h interfaces or __* variants thereof, as well as defining its own
interfaces, I think it might make sense to get all those optimized
versions included from include/math.h, not requiring a separate header
at all, before eliminating unused math_private.h includes - that
avoids a file quietly becoming less-optimized if someone adds a call
to one of those interfaces without restoring a math_private.h include
to that file.)

There is still a pitfall that if code uses plain fe* and __fe*
interfaces, but only includes fenv.h and not fenv_private.h or (before
this patch) math_private.h, it will compile on platforms with
exceptions and rounding modes but not get the optimized versions (and
possibly not compile) on platforms without exception and rounding mode
support, so making it easy to break the build for such platforms
accidentally.

I think it would be most natural to move the inlines / macros for fe*
and __fe* in the case of no exceptions and rounding modes into
include/fenv.h, so that all code including fenv.h with _ISOMAC not
defined automatically gets them.  Then fenv_private.h would be purely
the header for the libc_fe*, SET_RESTORE_ROUND etc. internal
interfaces and the risk of breaking the build on other platforms than
the one you tested on because of a missing fenv_private.h include
would be much reduced (and there would be some unused fenv_private.h
includes to remove along with unused math_private.h includes).

Tested for x86_64 and x86, and tested with build-many-glibcs.py that
installed stripped shared libraries are unchanged by this patch.

	* sysdeps/generic/math_private.h: Do not include <fenv_private.h>.
	* math/fromfp.h: Include <fenv_private.h>.
	* math/math-narrow.h: Likewise.
	* math/s_cexp_template.c: Likewise.
	* math/s_csin_template.c: Likewise.
	* math/s_csinh_template.c: Likewise.
	* math/s_ctan_template.c: Likewise.
	* math/s_ctanh_template.c: Likewise.
	* math/s_iseqsig_template.c: Likewise.
	* math/w_acos_compat.c: Likewise.
	* math/w_acosf_compat.c: Likewise.
	* math/w_acosl_compat.c: Likewise.
	* math/w_asin_compat.c: Likewise.
	* math/w_asinf_compat.c: Likewise.
	* math/w_asinl_compat.c: Likewise.
	* math/w_ilogb_template.c: Likewise.
	* math/w_j0_compat.c: Likewise.
	* math/w_j0f_compat.c: Likewise.
	* math/w_j0l_compat.c: Likewise.
	* math/w_j1_compat.c: Likewise.
	* math/w_j1f_compat.c: Likewise.
	* math/w_j1l_compat.c: Likewise.
	* math/w_jn_compat.c: Likewise.
	* math/w_jnf_compat.c: Likewise.
	* math/w_llogb_template.c: Likewise.
	* math/w_log10_compat.c: Likewise.
	* math/w_log10f_compat.c: Likewise.
	* math/w_log10l_compat.c: Likewise.
	* math/w_log2_compat.c: Likewise.
	* math/w_log2f_compat.c: Likewise.
	* math/w_log2l_compat.c: Likewise.
	* math/w_log_compat.c: Likewise.
	* math/w_logf_compat.c: Likewise.
	* math/w_logl_compat.c: Likewise.
	* sysdeps/aarch64/fpu/feholdexcpt.c: Likewise.
	* sysdeps/aarch64/fpu/fesetround.c: Likewise.
	* sysdeps/aarch64/fpu/fgetexcptflg.c: Likewise.
	* sysdeps/aarch64/fpu/ftestexcept.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_atan2.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_exp.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_exp2.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_gamma_r.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_jn.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_pow.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_remainder.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_sqrt.c: Likewise.
	* sysdeps/ieee754/dbl-64/gamma_product.c: Likewise.
	* sysdeps/ieee754/dbl-64/lgamma_neg.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_atan.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_fma.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_fmaf.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_llrint.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_llround.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_lrint.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_lround.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_nearbyint.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_sin.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_sincos.c: Likewise.
	* sysdeps/ieee754/dbl-64/s_tan.c: Likewise.
	* sysdeps/ieee754/dbl-64/wordsize-64/s_lround.c: Likewise.
	* sysdeps/ieee754/dbl-64/wordsize-64/s_nearbyint.c: Likewise.
	* sysdeps/ieee754/dbl-64/x2y2m1.c: Likewise.
	* sysdeps/ieee754/float128/float128_private.h: Likewise.
	* sysdeps/ieee754/flt-32/e_gammaf_r.c: Likewise.
	* sysdeps/ieee754/flt-32/e_j1f.c: Likewise.
	* sysdeps/ieee754/flt-32/e_jnf.c: Likewise.
	* sysdeps/ieee754/flt-32/lgamma_negf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_llrintf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_llroundf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_lrintf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_lroundf.c: Likewise.
	* sysdeps/ieee754/flt-32/s_nearbyintf.c: Likewise.
	* sysdeps/ieee754/k_standardl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/e_expl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/e_gammal_r.c: Likewise.
	* sysdeps/ieee754/ldbl-128/e_j1l.c: Likewise.
	* sysdeps/ieee754/ldbl-128/e_jnl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/gamma_productl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/lgamma_negl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_fmal.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_llrintl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_llroundl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_lrintl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_lroundl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_nearbyintl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/x2y2m1l.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_expl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_j1l.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_fmal.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_llrintl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_llroundl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_lrintl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_lroundl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_rintl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c: Likewise.
	* sysdeps/ieee754/ldbl-96/e_gammal_r.c: Likewise.
	* sysdeps/ieee754/ldbl-96/e_jnl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/gamma_productl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/lgamma_negl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_fma.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_fmal.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_llrintl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_llroundl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_lrintl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_lroundl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/x2y2m1l.c: Likewise.
	* sysdeps/powerpc/fpu/e_sqrt.c: Likewise.
	* sysdeps/powerpc/fpu/e_sqrtf.c: Likewise.
	* sysdeps/riscv/rv64/rvd/s_ceil.c: Likewise.
	* sysdeps/riscv/rv64/rvd/s_floor.c: Likewise.
	* sysdeps/riscv/rv64/rvd/s_nearbyint.c: Likewise.
	* sysdeps/riscv/rv64/rvd/s_round.c: Likewise.
	* sysdeps/riscv/rv64/rvd/s_roundeven.c: Likewise.
	* sysdeps/riscv/rv64/rvd/s_trunc.c: Likewise.
	* sysdeps/riscv/rvd/s_finite.c: Likewise.
	* sysdeps/riscv/rvd/s_fmax.c: Likewise.
	* sysdeps/riscv/rvd/s_fmin.c: Likewise.
	* sysdeps/riscv/rvd/s_fpclassify.c: Likewise.
	* sysdeps/riscv/rvd/s_isinf.c: Likewise.
	* sysdeps/riscv/rvd/s_isnan.c: Likewise.
	* sysdeps/riscv/rvd/s_issignaling.c: Likewise.
	* sysdeps/riscv/rvf/fegetround.c: Likewise.
	* sysdeps/riscv/rvf/feholdexcpt.c: Likewise.
	* sysdeps/riscv/rvf/fesetenv.c: Likewise.
	* sysdeps/riscv/rvf/fesetround.c: Likewise.
	* sysdeps/riscv/rvf/feupdateenv.c: Likewise.
	* sysdeps/riscv/rvf/fgetexcptflg.c: Likewise.
	* sysdeps/riscv/rvf/ftestexcept.c: Likewise.
	* sysdeps/riscv/rvf/s_ceilf.c: Likewise.
	* sysdeps/riscv/rvf/s_finitef.c: Likewise.
	* sysdeps/riscv/rvf/s_floorf.c: Likewise.
	* sysdeps/riscv/rvf/s_fmaxf.c: Likewise.
	* sysdeps/riscv/rvf/s_fminf.c: Likewise.
	* sysdeps/riscv/rvf/s_fpclassifyf.c: Likewise.
	* sysdeps/riscv/rvf/s_isinff.c: Likewise.
	* sysdeps/riscv/rvf/s_isnanf.c: Likewise.
	* sysdeps/riscv/rvf/s_issignalingf.c: Likewise.
	* sysdeps/riscv/rvf/s_nearbyintf.c: Likewise.
	* sysdeps/riscv/rvf/s_roundevenf.c: Likewise.
	* sysdeps/riscv/rvf/s_roundf.c: Likewise.
	* sysdeps/riscv/rvf/s_truncf.c: Likewise.
 2018-09-03 21:09:04 +00:00
Joseph Myers
688903eb3e Update copyright dates with scripts/update-copyrights. 
* All files with FSF copyright notices: Update copyright dates
	using scripts/update-copyrights.
	* locale/programs/charmap-kw.h: Regenerated.
	* locale/programs/locfile-kw.h: Likewise.
 2018-01-01 00:32:25 +00:00
Joseph Myers
bfff8b1bec Update copyright dates with scripts/update-copyrights. 2017-01-01 00:14:16 +00:00
Joseph Myers
f7a9f785e5 Update copyright dates with scripts/update-copyrights. 2016-01-04 16:05:18 +00:00
Joseph Myers
050f29c188 Fix lgamma (negative) inaccuracy (bug 2542, bug 2543, bug 2558). 
The existing implementations of lgamma functions (except for the ia64
versions) use the reflection formula for negative arguments.  This
suffers large inaccuracy from cancellation near zeros of lgamma (near
where the gamma function is +/- 1).

This patch fixes this inaccuracy.  For arguments above -2, there are
no zeros and no large cancellation, while for sufficiently large
negative arguments the zeros are so close to integers that even for
integers +/- 1ulp the log(gamma(1-x)) term dominates and cancellation
is not significant.  Thus, it is only necessary to take special care
about cancellation for arguments around a limited number of zeros.

Accordingly, this patch uses precomputed tables of relevant zeros,
expressed as the sum of two floating-point values.  The log of the
ratio of two sines can be computed accurately using log1p in cases
where log would lose accuracy.  The log of the ratio of two gamma(1-x)
values can be computed using Stirling's approximation (the difference
between two values of that approximation to lgamma being computable
without computing the two values and then subtracting), with
appropriate adjustments (which don't reduce accuracy too much) in
cases where 1-x is too small to use Stirling's approximation directly.

In the interval from -3 to -2, using the ratios of sines and of
gamma(1-x) can still produce too much cancellation between those two
parts of the computation (and that interval is also the worst interval
for computing the ratio between gamma(1-x) values, which computation
becomes more accurate, while being less critical for the final result,
for larger 1-x).  Because this can result in errors slightly above
those accepted in glibc, this interval is instead dealt with by
polynomial approximations.  Separate polynomial approximations to
(|gamma(x)|-1)(x-n)/(x-x0) are used for each interval of length 1/8
from -3 to -2, where n (-3 or -2) is the nearest integer to the
1/8-interval and x0 is the zero of lgamma in the relevant half-integer
interval (-3 to -2.5 or -2.5 to -2).

Together, the two approaches are intended to give sufficient accuracy
for all negative arguments in the problem range.  Outside that range,
the previous implementation continues to be used.

Tested for x86_64, x86, mips64 and powerpc.  The mips64 and powerpc
testing shows up pre-existing problems for ldbl-128 and ldbl-128ibm
with large negative arguments giving spurious "invalid" exceptions
(exposed by newly added tests for cases this patch doesn't affect the
logic for); I'll address those problems separately.

	[BZ #2542]
	[BZ #2543]
	[BZ #2558]
	* sysdeps/ieee754/dbl-64/e_lgamma_r.c (__ieee754_lgamma_r): Call
	__lgamma_neg for arguments from -28.0 to -2.0.
	* sysdeps/ieee754/flt-32/e_lgammaf_r.c (__ieee754_lgammaf_r): Call
	__lgamma_negf for arguments from -15.0 to -2.0.
	* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
	Call __lgamma_negl for arguments from -48.0 or -50.0 to -2.0.
	* sysdeps/ieee754/ldbl-96/e_lgammal_r.c (__ieee754_lgammal_r):
	Call __lgamma_negl for arguments from -33.0 to -2.0.
	* sysdeps/ieee754/dbl-64/lgamma_neg.c: New file.
	* sysdeps/ieee754/dbl-64/lgamma_product.c: Likewise.
	* sysdeps/ieee754/flt-32/lgamma_negf.c: Likewise.
	* sysdeps/ieee754/flt-32/lgamma_productf.c: Likewise.
	* sysdeps/ieee754/ldbl-128/lgamma_negl.c: Likewise.
	* sysdeps/ieee754/ldbl-128/lgamma_productl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/lgamma_negl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/lgamma_product.c: Likewise.
	* sysdeps/ieee754/ldbl-96/lgamma_productl.c: Likewise.
	* sysdeps/generic/math_private.h (__lgamma_negf): New prototype.
	(__lgamma_neg): Likewise.
	(__lgamma_negl): Likewise.
	(__lgamma_product): Likewise.
	(__lgamma_productl): Likewise.
	* math/Makefile (libm-calls): Add lgamma_neg and lgamma_product.
	* math/auto-libm-test-in: Add more tests of lgamma.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
 2015-09-10 22:27:58 +00:00