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4f8f819975
We approximate pi with more than float precision using pi_hi+pi_lo in the usual way (pi_hi is actually spelled pi in the source code), and expect (float)0.5*pi_lo to give the low part of the corresponding approximation for pi/2. However, the high part for pi/2 (pi_o_2) is rounded to nearest, which happens to round up, while the high part for pi was rounded down. Thus pi_o_2+(float)0.5*pi (in infinite precision) was a very bad approximation for pi/2 -- the low term has the wrong sign and increases the error drom less than half an ULP to a full ULP. This fix rounds up instead of down for pi_hi. Consistently rounding down instead of up should work, and is the method used in e_acosf.c and e_asinf.c. The reason for the difference is that we sometimes want to return precisely pi/2 in e_atan2f.c, so it is convenient to have a correctly rounded (to nearest) value for pi/2 in a variable. a_acosf.c and e_asinf.c also differ in directly approximating pi/2 instead pi; they multiply by 2.0 instead of dividing by 0.5 to convert the approximation. These complications are not directly visible in the double precision versions because rounding to nearest happens to round down. |
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| bin | ||
| contrib | ||
| crypto | ||
| etc | ||
| games | ||
| gnu | ||
| include | ||
| kerberos5 | ||
| lib | ||
| libexec | ||
| release | ||
| rescue | ||
| sbin | ||
| secure | ||
| share | ||
| sys | ||
| tools | ||
| usr.bin | ||
| usr.sbin | ||
| COPYRIGHT | ||
| installworld_newk | ||
| installworld_oldk | ||
| MAINTAINERS | ||
| Makefile | ||
| Makefile.inc1 | ||
| README | ||
| UPDATING | ||
| UPDATING.64BTT | ||
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