11cba99f67
and add a comment about related magic (many lines)). __kernel_cos[f]() needs a trick to reduce the error to below 1 ulp when |x| >= 0.3 for the range-reduced x. Modulo other bugs, naive code that doesn't use the trick would have an error of >= 1 ulp in about 0.00006% of cases when |x| >= 0.3 for the unreduced x, with a maximum relative error of about 1.03 ulps. Mistransation of the trick from the double precision case resulted in errors in about 0.2% of cases, with a maximum relative error of about 1.3 ulps. The mistranslation involved not doing implicit masking of the 32-bit float word corresponding to to implicit masking of the lower 32-bit double word by clearing it. sinf() uses __kernel_cosf() for half of all cases so its errors from this bug are similar. tanf() is not affected. The error bounds in the above and in my other recent commit messages are for amd64. Extra precision for floats on i386's accidentally masks this bug, but only if k_cosf.c is compiled with -O. Although the extra precision helps here, this is accidental and depends on longstanding gcc precision bugs (not clipping extra precision on assignment...), and the gcc bugs are mostly avoided by compiling without -O. I now develop libm mainly on amd64 systems to simplify error detection and debugging.
This is the top level of the FreeBSD source directory. This file was last revised on: $FreeBSD$ For copyright information, please see the file COPYRIGHT in this directory (additional copyright information also exists for some sources in this tree - please see the specific source directories for more information). The Makefile in this directory supports a number of targets for building components (or all) of the FreeBSD source tree, the most commonly used one being ``world'', which rebuilds and installs everything in the FreeBSD system from the source tree except the kernel, the kernel-modules and the contents of /etc. The ``buildkernel'' and ``installkernel'' targets build and install the kernel and the modules (see below). Please see the top of the Makefile in this directory for more information on the standard build targets and compile-time flags. Building a kernel is a somewhat more involved process, documentation for which can be found at: http://www.freebsd.org/doc/en_US.ISO8859-1/books/handbook/kernelconfig.html And in the config(8) man page. Note: If you want to build and install the kernel with the ``buildkernel'' and ``installkernel'' targets, you might need to build world before. More information is available in the handbook. The sample kernel configuration files reside in the sys/<arch>/conf sub-directory (assuming that you've installed the kernel sources), the file named GENERIC being the one used to build your initial installation kernel. The file NOTES contains entries and documentation for all possible devices, not just those commonly used. It is the successor of the ancient LINT file, but in contrast to LINT, it is not buildable as a kernel but a pure reference and documentation file. Source Roadmap: --------------- bin System/user commands. contrib Packages contributed by 3rd parties. crypto Cryptography stuff (see crypto/README). etc Template files for /etc. games Amusements. gnu Various commands and libraries under the GNU Public License. Please see gnu/COPYING* for more information. include System include files. kerberos5 Kerberos5 (Heimdal) package. lib System libraries. libexec System daemons. release Release building Makefile & associated tools. sbin System commands. secure Cryptographic libraries and commands. share Shared resources. sys Kernel sources. tools Utilities for regression testing and miscellaneous tasks. usr.bin User commands. usr.sbin System administration commands. For information on synchronizing your source tree with one or more of the FreeBSD Project's development branches, please see: http://www.freebsd.org/doc/en_US.ISO8859-1/books/handbook/synching.html