| Commit message (Collapse) | Author | Age | Files | Lines |
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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.
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If you remove the "override CFLAGS += -Wno-uninitialized" in
math/Makefile, you get errors from lgamma implementations of the form:
../sysdeps/ieee754/dbl-64/e_lgamma_r.c: In function '__ieee754_lgamma_r':
../sysdeps/ieee754/dbl-64/e_lgamma_r.c:297:13: error: 'nadj' may be used uninitialized in this function [-Werror=maybe-uninitialized]
if(hx<0) r = nadj - r;
This is one of the standard kinds of false positive uninitialized
warnings: nadj is set under a certain condition, and then later used
under the same condition. This patch uses DIAG_* macros to suppress
the warning on the use of nadj. The ldbl-128 / ldbl-128ibm
implementation has a substantially different structure that avoids
this issue.
Tested for x86_64. (In fact this patch eliminates the need for that
-Wno-uninitialized on x86_64, but I want to test on more architectures
before removing it.)
* sysdeps/ieee754/dbl-64/e_lgamma_r.c: Include <libc-internal.h>.
(__ieee754_lgamma_r): Ignore uninitialized warnings around use of
NADJ.
* sysdeps/ieee754/flt-32/e_lgammaf_r.c: Include <libc-internal.h>.
(__ieee754_lgammaf_r): Ignore uninitialized warnings around use of
NADJ.
* sysdeps/ieee754/ldbl-96/e_lgammal_r.c: Include <libc-internal.h>.
(__ieee754_lgammal_r): Ignore uninitialized warnings around use of
NADJ.
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Entire tree edited via find | grep | sed.
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libm is now somewhat integrated with gcc's -ffinite-math-only option
and lots of the wrapper functions have been optimized.
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* sysdeps/ieee754/dbl-64/e_lgamma_r.c: Fix *signgamp for -0.0.
* sysdeps/ieee754/flt-32/e_lgammaf_r.c: Likewise.
* sysdeps/ieee754/ldbl-96/e_lgammal_r.c: Likewise.
* math/libm-test.inc: Add test for this case.
Half the patch by Christian Iseli <christian.iseli@licr.org>.
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wording at request of copyright holder Stephen Moshier.
* sysdeps/ieee754/ldbl-128/e_acosl.c: Likewise.
* sysdeps/ieee754/ldbl-128/e_asinl.c: Likewise.
* sysdeps/ieee754/ldbl-128/e_coshl.c: Likewise.
* sysdeps/ieee754/ldbl-128/e_jnl.c: Likewise.
* sysdeps/ieee754/ldbl-128/e_powl.c: Likewise.
* sysdeps/ieee754/ldbl-128/e_sinhl.c: Likewise.
* sysdeps/ieee754/ldbl-128/k_tanl.c: Likewise.
* sysdeps/ieee754/ldbl-128/s_erfl.c: Likewise.
* sysdeps/ieee754/ldbl-96/e_asinl.c: Likewise.
* sysdeps/ieee754/ldbl-96/e_j0l.c: Likewise.
* sysdeps/ieee754/ldbl-96/e_j1l.c: Likewise.
* sysdeps/ieee754/ldbl-96/e_jnl.c: Likewise.
* sysdeps/ieee754/ldbl-96/e_lgammal_r.c: Likewise.
* sysdeps/ieee754/ldbl-96/s_erfl.c: Likewise.
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* crypt/crypt.c: Changed copying permission notice to Lesser GPL
from Library GPL.
* crypt/crypt_util.c: Likewise.
* crypt/ufc.c: Likewise.
* elf/dl-conflict.c: Likewise.
* elf/dl-iteratephdr.c: Likewise.
* iconv/iconvconfig.h: Likewise.
* linuxthreads/Examples/ex10.c: Likewise.
* linuxthreads/Examples/ex11.c: Likewise.
* linuxthreads/Examples/ex13.c: Likewise.
* linuxthreads/Examples/ex8.c: Likewise.
* linuxthreads/Examples/ex9.c: Likewise.
* linuxthreads/barrier.c: Likewise.
* linuxthreads/events.c: Likewise.
* linuxthreads/lockfile.c: Likewise.
* linuxthreads/no-tsd.c: Likewise.
* linuxthreads/pt-machine.c: Likewise.
* linuxthreads/ptclock_gettime.c: Likewise.
* linuxthreads/ptclock_settime.c: Likewise.
* linuxthreads/rwlock.c: Likewise.
* linuxthreads/sysdeps/alpha/pspinlock.c: Likewise.
* linuxthreads/sysdeps/alpha/pt-machine.h: Likewise.
* linuxthreads/sysdeps/arm/pspinlock.c: Likewise.
* linuxthreads/sysdeps/arm/pt-machine.h: Likewise.
* linuxthreads/sysdeps/cris/pspinlock.c: Likewise.
* linuxthreads/sysdeps/cris/pt-machine.h: Likewise.
* linuxthreads/sysdeps/hppa/pspinlock.c: Likewise.
* linuxthreads/sysdeps/hppa/pt-machine.h: Likewise.
* linuxthreads/sysdeps/i386/i686/pt-machine.h: Likewise.
* linuxthreads/sysdeps/i386/pspinlock.c: Likewise.
* linuxthreads/sysdeps/i386/pt-machine.h: Likewise.
* linuxthreads/sysdeps/i386/useldt.h: Likewise.
* linuxthreads/sysdeps/ia64/pspinlock.c: Likewise.
* linuxthreads/sysdeps/ia64/pt-machine.h: Likewise.
* linuxthreads/sysdeps/m68k/pspinlock.c: Likewise.
* linuxthreads/sysdeps/m68k/pt-machine.h: Likewise.
* linuxthreads/sysdeps/mips/pspinlock.c: Likewise.
* linuxthreads/sysdeps/mips/pt-machine.h: Likewise.
* linuxthreads/sysdeps/powerpc/pspinlock.c: Likewise.
* linuxthreads/sysdeps/powerpc/pt-machine.h: Likewise.
* linuxthreads/sysdeps/pthread/bits/initspin.h: Likewise.
* linuxthreads/sysdeps/pthread/bits/libc-lock.h: Likewise.
* linuxthreads/sysdeps/pthread/bits/libc-tsd.h: Likewise.
* linuxthreads/sysdeps/pthread/getcpuclockid.c: Likewise.
* linuxthreads/sysdeps/pthread/posix-timer.h: Likewise.
* linuxthreads/sysdeps/pthread/timer_create.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_delete.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_getoverr.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_gettime.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_routines.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_settime.c: Likewise.
* linuxthreads/sysdeps/pthread/tst-timer.c: Likewise.
* linuxthreads/sysdeps/s390/pspinlock.c: Likewise.
* linuxthreads/sysdeps/s390/s390-32/pt-machine.h: Likewise.
* linuxthreads/sysdeps/s390/s390-64/pt-machine.h: Likewise.
* linuxthreads/sysdeps/sh/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sh/pt-machine.h: Likewise.
* linuxthreads/sysdeps/sparc/sparc32/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sparc/sparc32/pt-machine.h: Likewise.
* linuxthreads/sysdeps/sparc/sparc32/sparcv9/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sparc/sparc64/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sparc/sparc64/pt-machine.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/bits/local_lim.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/bits/posix_opt.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/bits/sigthread.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/hppa/bits/initspin.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/i386/bits/posix_opt.h: Likewise.
* linuxthreads/tststack.c: Likewise.
* linuxthreads/unload.c: Likewise.
* linuxthreads/weaks.c: Likewise.
* linuxthreads/wrapsyscall.c: Likewise.
* malloc/arena.c: Likewise.
* malloc/hooks.c: Likewise.
* malloc/malloc.c: Likewise.
* posix/glob/Makefile.ami: Likewise.
* posix/glob/Makefile.in: Likewise.
* stdlib/gmp-impl.h: Likewise.
* stdlib/gmp.h: Likewise.
* sysdeps/generic/dl-iteratephdr-static.c: Likewise.
* sysdeps/generic/strnlen.c: Likewise.
* sysdeps/mach/hurd/powerpc/bits/sigcontext.h: Likewise.
* sysdeps/mach/hurd/recvmsg.c: Likewise.
* sysdeps/mach/hurd/sendmsg.c: Likewise.
* sysdeps/mach/hurd/spawni.c: Likewise.
* sysdeps/mach/powerpc/machine-sp.h: Likewise.
* sysdeps/mach/powerpc/sysdep.h: Likewise.
* sysdeps/mach/powerpc/thread_state.h: Likewise.
* sysdeps/unix/bsd/bsd4.4/bits/socket.h: Likewise.
* sysdeps/unix/sysv/linux/ia64/dl-iteratephdr-static.c: Likewise.
* sysdeps/x86_64/gmp-mparam.h: Likewise.
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correctly.
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2002-01-07 Stephen L Moshier <moshier@mediaone.net>
* sysdeps/ieee754/ldbl-96/s_erfl.c (erfcl): Fix K&R header.
* sysdeps/ieee754/ldbl-96/e_lgammal_r.c (sin_pi): Fix typo in test
for x < 0.25 and restore original range reduction method.
(__ieee754_lgammal_r): Make sure signgam is set before returning.
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* sysdeps/ieee754/ldbl-96/e_lgammal_r.c: New file.
Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>.
* sysdeps/ieee754/ldbl-96/e_gammal_r.c: Fix handling of boundary cases.
* sysdeps/ieee754/dbl-64/e_gamma_r.c: Always initialize sign variable.
* sysdeps/ieee754/flt-32/e_gammaf_r.c: Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Adjust after addition of lgammal.
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