mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-23 17:53:37 +08:00
050f29c188
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. |
||
|---|---|---|
| argp | ||
| assert | ||
| benchtests | ||
| bits | ||
| catgets | ||
| conf | ||
| conform | ||
| crypt | ||
| csu | ||
| ctype | ||
| debug | ||
| dirent | ||
| dlfcn | ||
| elf | ||
| gmon | ||
| gnulib | ||
| grp | ||
| gshadow | ||
| hesiod | ||
| hurd | ||
| iconv | ||
| iconvdata | ||
| include | ||
| inet | ||
| intl | ||
| io | ||
| libidn | ||
| libio | ||
| locale | ||
| localedata | ||
| login | ||
| mach | ||
| malloc | ||
| manual | ||
| math | ||
| mathvec | ||
| misc | ||
| nis | ||
| nptl | ||
| nptl_db | ||
| nscd | ||
| nss | ||
| po | ||
| posix | ||
| pwd | ||
| resolv | ||
| resource | ||
| rt | ||
| scripts | ||
| setjmp | ||
| shadow | ||
| signal | ||
| socket | ||
| soft-fp | ||
| stdio-common | ||
| stdlib | ||
| streams | ||
| string | ||
| sunrpc | ||
| sysdeps | ||
| sysvipc | ||
| termios | ||
| time | ||
| timezone | ||
| wcsmbs | ||
| wctype | ||
| .gitattributes | ||
| .gitignore | ||
| abi-tags | ||
| aclocal.m4 | ||
| BUGS | ||
| ChangeLog | ||
| ChangeLog.1 | ||
| ChangeLog.2 | ||
| ChangeLog.3 | ||
| ChangeLog.4 | ||
| ChangeLog.5 | ||
| ChangeLog.6 | ||
| ChangeLog.7 | ||
| ChangeLog.8 | ||
| ChangeLog.9 | ||
| ChangeLog.10 | ||
| ChangeLog.11 | ||
| ChangeLog.12 | ||
| ChangeLog.13 | ||
| ChangeLog.14 | ||
| ChangeLog.15 | ||
| ChangeLog.16 | ||
| ChangeLog.17 | ||
| ChangeLog.old-ports | ||
| ChangeLog.old-ports-aarch64 | ||
| ChangeLog.old-ports-aix | ||
| ChangeLog.old-ports-alpha | ||
| ChangeLog.old-ports-am33 | ||
| ChangeLog.old-ports-arm | ||
| ChangeLog.old-ports-cris | ||
| ChangeLog.old-ports-hppa | ||
| ChangeLog.old-ports-ia64 | ||
| ChangeLog.old-ports-linux-generic | ||
| ChangeLog.old-ports-m68k | ||
| ChangeLog.old-ports-microblaze | ||
| ChangeLog.old-ports-mips | ||
| ChangeLog.old-ports-powerpc | ||
| ChangeLog.old-ports-tile | ||
| config.h.in | ||
| config.make.in | ||
| configure | ||
| configure.ac | ||
| CONFORMANCE | ||
| COPYING | ||
| COPYING.LIB | ||
| cppflags-iterator.mk | ||
| extra-lib.mk | ||
| extra-modules.mk | ||
| gen-locales.mk | ||
| INSTALL | ||
| libc-abis | ||
| LICENSES | ||
| Makeconfig | ||
| Makefile | ||
| Makefile.in | ||
| Makerules | ||
| NAMESPACE | ||
| NEWS | ||
| o-iterator.mk | ||
| PROJECTS | ||
| README | ||
| Rules | ||
| shlib-versions | ||
| test-skeleton.c | ||
| version.h | ||
| WUR-REPORT | ||
This directory contains the sources of the GNU C Library. See the file "version.h" for what release version you have. The GNU C Library is the standard system C library for all GNU systems, and is an important part of what makes up a GNU system. It provides the system API for all programs written in C and C-compatible languages such as C++ and Objective C; the runtime facilities of other programming languages use the C library to access the underlying operating system. In GNU/Linux systems, the C library works with the Linux kernel to implement the operating system behavior seen by user applications. In GNU/Hurd systems, it works with a microkernel and Hurd servers. The GNU C Library implements much of the POSIX.1 functionality in the GNU/Hurd system, using configurations i[4567]86-*-gnu. The current GNU/Hurd support requires out-of-tree patches that will eventually be incorporated into an official GNU C Library release. When working with Linux kernels, this version of the GNU C Library requires Linux kernel version 2.6.32 or later. Also note that the shared version of the libgcc_s library must be installed for the pthread library to work correctly. The GNU C Library supports these configurations for using Linux kernels: aarch64*-*-linux-gnu alpha*-*-linux-gnu arm-*-linux-gnueabi hppa-*-linux-gnu Not currently functional without patches. i[4567]86-*-linux-gnu x86_64-*-linux-gnu Can build either x86_64 or x32 ia64-*-linux-gnu m68k-*-linux-gnu microblaze*-*-linux-gnu mips-*-linux-gnu mips64-*-linux-gnu powerpc-*-linux-gnu Hardware or software floating point, BE only. powerpc64*-*-linux-gnu Big-endian and little-endian. s390-*-linux-gnu s390x-*-linux-gnu sh[34]-*-linux-gnu sparc*-*-linux-gnu sparc64*-*-linux-gnu tilegx-*-linux-gnu tilepro-*-linux-gnu If you are interested in doing a port, please contact the glibc maintainers; see http://www.gnu.org/software/libc/ for more information. See the file INSTALL to find out how to configure, build, and install the GNU C Library. You might also consider reading the WWW pages for the C library at http://www.gnu.org/software/libc/. The GNU C Library is (almost) completely documented by the Texinfo manual found in the `manual/' subdirectory. The manual is still being updated and contains some known errors and omissions; we regret that we do not have the resources to work on the manual as much as we would like. For corrections to the manual, please file a bug in the `manual' component, following the bug-reporting instructions below. Please be sure to check the manual in the current development sources to see if your problem has already been corrected. Please see http://www.gnu.org/software/libc/bugs.html for bug reporting information. We are now using the Bugzilla system to track all bug reports. This web page gives detailed information on how to report bugs properly. The GNU C Library is free software. See the file COPYING.LIB for copying conditions, and LICENSES for notices about a few contributions that require these additional notices to be distributed. License copyright years may be listed using range notation, e.g., 1996-2015, indicating that every year in the range, inclusive, is a copyrightable year that would otherwise be listed individually.