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f67f9c9af2
asin and acos have slow paths for rounding the last bit that cause some calls to be 500-1500x slower than average calls. These slow paths are rare, a test of a trillion (1.000.000.000.000) random inputs between -1 and 1 showed 32870 slow calls for acos and 4473 for asin, with most occurrences between -1.0 .. -0.9 and 0.9 .. 1.0. The slow paths claim correct rounding and use __sin32() and __cos32() (which compare two result candidates and return the closest one) as the final step, with the second result candidate (res1) having a small offset applied from res. This suggests that res and res1 are intended to be 1 ULP apart (which makes sense for rounding), barring bugs, allowing us to pick either one and still remain within 1 ULP of the exact result. Remove the slow paths as the accuracy is better than 1 ULP even without them, which is enough for glibc. Also remove code comments claiming correctly rounded results. After slow path removal, checking the accuracy of 14.400.000.000 random asin() and acos() inputs showed only three incorrectly rounded (error > 0.5 ULP) results: - asin(-0x1.ee2b43286db75p-1) (0.500002 ULP, same as before) - asin(-0x1.f692ba202abcp-4) (0.500003 ULP, same as before) - asin(-0x1.9915e876fc062p-1) (0.50000000001 ULP, previously exact) The first two had the same error even before this commit, and they did not use the slow path at all. Checking 4934 known randomly found previously-slow-path asin inputs shows 25 calls with incorrectly rounded results, with a maximum error of 0.500000002 ULP (for 0x1.fcd5742999ab8p-1). The previous slow-path code rounded all these inputs correctly (error < 0.5 ULP). The observed average speed increase was 130x. Checking 36240 known randomly found previously-slow-path acos inputs shows 42 calls with incorrectly rounded results, with a maximum error of 0.500000008 ULP (for 0x1.f63845056f35ep-1). The previous "exact" slow-path code showed 34 calls with incorrectly rounded results, with the same maximum error of 0.500000008 ULP (for 0x1.f63845056f35ep-1). The observed average speed increase was 130x. The functions could likely be trimmed more while keeping acceptable accuracy, but this at least gets rid of the egregiously slow cases. Tested on x86_64. |
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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. When working with Linux kernels, this version of the GNU C Library requires Linux kernel version 3.2 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 arc*-*-linux-gnu arm-*-linux-gnueabi csky-*-linux-gnuabiv2 hppa-*-linux-gnu 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 riscv32-*-linux-gnu riscv64-*-linux-gnu sh[34]-*-linux-gnu sparc*-*-linux-gnu sparc64*-*-linux-gnu If you are interested in doing a port, please contact the glibc maintainers; see https://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 https://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 https://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.