freebsd kernel with SKQ
11d5bb39af
sqrt(2)/2-1. For log1p(), fixed the approximation to sqrt(2)/2-1.
The end result is to fix an error of 1.293 ulps in
log1pf(0.41421395540 (hex 0x3ed413da))
and an error of 1.783 ulps in
log1p(-0.292893409729003961761) (hex 0x12bec4 00000001)).
The former was the only error of > 1 ulp for log1pf() and the latter
is the only such error that I know of for log1p().
The approximations don't need to be very accurate, but the last 2 need
to be related to the first and be rounded up a little (even more than
1 ulp for sqrt(2)/2-1) for the following implementation-detail reason:
when the arg (x) is not between (the approximations to) sqrt(2)/2-1
and sqrt(2)-1, we commit to using a correction term, but we only
actually use it if 1+x is between sqrt(2)/2 and sqrt(2) according to
the first approximation. Thus we must ensure that
!(sqrt(2)/2-1 < x < sqrt(2)-1) implies !(sqrt(2)/2 < x+1 < sqrt(2)),
where all the sqrt(2)'s are really slightly different approximations
to sqrt(2) and some of the "<"'s are really "<="'s. This was not done.
In log1pf(), the last 2 approximations were rounded up by about 6 ulps
more than needed relative to a good approximation to sqrt(2), but the
actual approximation to sqrt(2) was off by 3 ulps. The approximation
to sqrt(2)-1 ended up being 4 ulps too small, so the algoritm was
broken in 4 cases. The result happened to be broken in 1 case. This
is fixed by using a natural approximation to sqrt(2) and derived
approximations for the others.
In logf(), all the approximations made sense, but the approximation
to sqrt(2)/2-1 was 2 ulps too small (a tiny amount, since we compare
with a granularity of 2**32 ulps), so the algorithm was broken in 2
cases. The result was broken in 1 case. This is fixed by rounding
up the approximation to sqrt(2)/2-1 by 2**32 ulps, so 2**32 cases are
now handled a little differently (still correctly according to my
assertion that the approximations don't need to be very accurate, but
this has not been checked).
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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 | ||
| LOCKS | ||
| MAINTAINERS | ||
| Makefile | ||
| Makefile.inc1 | ||
| ObsoleteFiles.inc | ||
| README | ||
| UPDATING | ||
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