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This patch fixes bug 16354, spurious underflows from cosh when a tiny argument is passed to expm1 and expm1 correctly underflows although the final result of cosh should be 1. As noted in that bug, some cases are latent because of expm1 implementations not raising underflow (bug 16353), but all the implementations are fixed similarly. They already contained checks for tiny arguments, but the checks were too late to avoid underflow from expm1 (although they would avoid underflow from subsequent squaring of the result of expm1); they are moved before the expm1 calls. The thresholds used for considering arguments tiny are not particularly consistent in how they relate to the precision of the floating-point format in question. They are, however, all sufficient to ensure that the round-to-nearest result of cosh is indeed 1 below the threshold (although sometimes they are smaller than necessary). But the previous logic did not return 1, but the previously computed 1 + expm1(abs(x)) value. And the thresholds in the ldbl-128 and ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for that value to be 1. So by moving the test for tiny arguments, and consequently returning 1 directly now the expm1 value hasn't been computed by that point, this patch also fixes bug 17061, the (large number of ulps) inaccuracy for small arguments in those implementations. Tests for that bug are duly added. Tested x86_64 and x86 and ulps updated accordingly. Also tested for mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes. [BZ #16354] [BZ #17061] * sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for small arguments before calling __expm1. * sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for small arguments before calling __expm1f. * sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for small arguments before calling __expm1l. * sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl): Likewise. * sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise. * math/auto-libm-test-in: Add more cosh tests. Do not allow spurious underflow for some cosh tests. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. |
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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 The code for other CPU configurations supported by volunteers outside of the core glibc maintenance effort is contained in the `ports' add-on, located in the `ports' subdirectory of the source tree. 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., 2000-2013, indicating that every year in the range, inclusive, is a copyrightable year that would otherwise be listed individually.