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The current approach tracks math maximum supported errors by explicitly
setting them per function and architecture. On newer implementations or
new compiler versions, the file is updated with newer values if it
shows higher results. The idea is to track the maximum known error, to
update the manual with the obtained values.
The constant libm-test-ulps shows little value, where it is usually a
mechanical change done by the maintainer, for past releases it is
usually ignored whether the ulp change resulted from a compiler
regression, and the math tests already have a maximum ulp error that
triggers a regression.
It was shown by a recent update after the new acosf [1] implementation
that is correctly rounded, where the libm-test-ulps was indeed from a
compiler issue.
This patch removes all arch-specific libm-test-ulps, adds system generic
libm-test-ulps where applicable, and changes its semantics. The generic
files now track specific implementation constraints, like if it is
expected to be correctly rounded, or if the system-specific has
different error expectations.
Now multiple libm-test-ulps can be defined, and system-specific
overrides generic implementation. This is for the case where
arch-specific implementation might show worse precision than generic
implementation, for instance, the cbrtf on i686.
Regressions are only reported if the implementation shows larger errors
than 9 ulps (13 for IBM long double) unless it is overridden by
libm-test-ulps and the maximum error is not printed at the end of tests.
The regen-ulps rule is also removed since it does not make sense to
update the libm-test-ulps automatically.
The manual error table is also removed, Paul Zimmermann and others have
been tracking libm precision with a more comprehensive analysis for some
releases; so link to his work instead.
[1] https://sourceware.org/git/?p=glibc.git;a=commit;h=9cc9f8e11e8fb8f54f1e84d9f024917634a78201
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The manual contained several instances of incorrect formatting
that were correct texinfo but produced incorrectly rendered manuals
or incorrect behaviour from the tooling.
The most important was incorrect quoting of function returns
by failing to use {} to quote the return. The impact of this
mistake means that 'info libc func' does not jump to the function
in question but instead to the introductory page under the assumption
that func doesn't exist. The function returns are now correctly
quoted.
The second issue was the use of a category specifier with
@deftypefun which doesn't accept a category specifier. If a category
specifier is required then @deftypefn needs to be used. This is
corrected by changing the command to @deftypefn for such functions
that used {Deprecated function} as a category.
The last issue is a missing space between the function name and the
arguments which results in odd function names like "epoll_wait(int"
instead of "epoll_wait". This also impacts the use of 'info libc'
and is corrected.
We additionally remove ';' from the end of function arguments and
add an 'int' return type for dprintf.
Lastly we add a new test check-deftype.sh which verifies the expected
formatting of @deftypefun, @deftypefunx, @deftypefn, and
@deftypefnx. The new test is also run as the summary file is
generated to ensure we don't generate incorrect results.
The existing check-safety.sh is also run directly as a test to increase
coverage since the existing tests only ran on manual install.
The new tests now run as part of the standard "make check" that
pre-commit CI runs and developers should run.
No regressions on x86_64.
HTML and PDF rendering reviewed and looks correct for all changes.
Reviewed-by: H.J. Lu <hjl.tools@gmail.com>
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The purpose of this patch is to add some system calls that (1) aren't
otherwise documented, and (2) are merely redirected to the kernel, so
can refer to their documentation; and define a standard way of doing
so in the future. A more detailed explaination of how system calls
are wrapped is added along with reference to the Linux Man-Pages
project.
Default version of man-pages is in configure.ac but can be overridden
by --with-man-pages=X.Y
Reviewed-by: Alejandro Colomar <alx@kernel.org>
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C23 adds a header <stdbit.h> with various functions and type-generic
macros for bit-manipulation of unsigned integers (plus macro defines
related to endianness). Implement this header for glibc.
The functions have both inline definitions in the header (referenced
by macros defined in the header) and copies with external linkage in
the library (which are implemented in terms of those macros to avoid
duplication). They are documented in the glibc manual. Tests, as
well as verifying results for various inputs (of both the macros and
the out-of-line functions), verify the types of those results (which
showed up a bug in an earlier version with the type-generic macro
stdc_has_single_bit wrongly returning a promoted type), that the
macros can be used at top level in a source file (so don't use ({})),
that they evaluate their arguments exactly once, and that the macros
for the type-specific functions have the expected implicit conversions
to the relevant argument type.
Jakub previously referred to -Wconversion warnings in type-generic
macros, so I've included a test with -Wconversion (but the only
warnings I saw and fixed from that test were actually in inline
functions in the <stdbit.h> header - not anything coming from use of
the type-generic macros themselves).
This implementation of the type-generic macros does not handle
unsigned __int128, or unsigned _BitInt types with a width other than
that of a standard integer type (and C23 doesn't require the header to
handle such types either). Support for those types, using the new
type-generic built-in functions Jakub's added for GCC 14, can
reasonably be added in a followup (along of course with associated
tests).
This implementation doesn't do anything special to handle C++, or have
any tests of functionality in C++ beyond the existing tests that all
headers can be compiled in C++ code; it's not clear exactly what form
this header should take in C++, but probably not one using macros.
DIS ballot comment AT-107 asks for the word "count" to be added to the
names of the stdc_leading_zeros, stdc_leading_ones,
stdc_trailing_zeros and stdc_trailing_ones functions and macros. I
don't think it's likely to be accepted (accepting any technical
comments would mean having an FDIS ballot), but if it is accepted at
the WG14 meeting (22-26 January in Strasbourg, starting with DIS
ballot comment handling) then there would still be time to update
glibc for the renaming before the 2.39 release.
The new functions and header are placed in the stdlib/ directory in
glibc, rather than creating a new toplevel stdbit/ or putting them in
string/ alongside ffs.
Tested for x86_64 and x86.
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I used these shell commands:
../glibc/scripts/update-copyrights $PWD/../gnulib/build-aux/update-copyright
(cd ../glibc && git commit -am"[this commit message]")
and then ignored the output, which consisted lines saying "FOO: warning:
copyright statement not found" for each of 7061 files FOO.
I then removed trailing white space from math/tgmath.h,
support/tst-support-open-dev-null-range.c, and
sysdeps/x86_64/multiarch/strlen-vec.S, to work around the following
obscure pre-commit check failure diagnostics from Savannah. I don't
know why I run into these diagnostics whereas others evidently do not.
remote: *** 912-#endif
remote: *** 913:
remote: *** 914-
remote: *** error: lines with trailing whitespace found
...
remote: *** error: sysdeps/unix/sysv/linux/statx_cp.c: trailing lines
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It can be used to speed up the libgcc unwinder, and the internal
_dl_find_dso_for_object function (which is used for caller
identification in dlopen and related functions, and in dladdr).
_dl_find_object is in the internal namespace due to bug 28503.
If libgcc switches to _dl_find_object, this namespace issue will
be fixed. It is located in libc for two reasons: it is necessary
to forward the call to the static libc after static dlopen, and
there is a link ordering issue with -static-libgcc and libgcc_eh.a
because libc.so is not a linker script that includes ld.so in the
glibc build tree (so that GCC's internal -lc after libgcc_eh.a does
not pick up ld.so).
It is necessary to do the i386 customization in the
sysdeps/x86/bits/dl_find_object.h header shared with x86-64 because
otherwise, multilib installations are broken.
The implementation uses software transactional memory, as suggested
by Torvald Riegel. Two copies of the supporting data structures are
used, also achieving full async-signal-safety.
Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
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I used these shell commands:
../glibc/scripts/update-copyrights $PWD/../gnulib/build-aux/update-copyright
(cd ../glibc && git commit -am"[this commit message]")
and then ignored the output, which consisted lines saying "FOO: warning:
copyright statement not found" for each of 6694 files FOO.
I then removed trailing white space from benchtests/bench-pthread-locks.c
and iconvdata/tst-iconv-big5-hkscs-to-2ucs4.c, to work around this
diagnostic from Savannah:
remote: *** pre-commit check failed ...
remote: *** error: lines with trailing whitespace found
remote: error: hook declined to update refs/heads/master
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Also, change sources.redhat.com to sourceware.org.
This patch was automatically generated by running the following shell
script, which uses GNU sed, and which avoids modifying files imported
from upstream:
sed -ri '
s,(http|ftp)(://(.*\.)?(gnu|fsf|sourceware)\.org($|[^.]|\.[^a-z])),https\2,g
s,(http|ftp)(://(.*\.)?)sources\.redhat\.com($|[^.]|\.[^a-z]),https\2sourceware.org\4,g
' \
$(find $(git ls-files) -prune -type f \
! -name '*.po' \
! -name 'ChangeLog*' \
! -path COPYING ! -path COPYING.LIB \
! -path manual/fdl-1.3.texi ! -path manual/lgpl-2.1.texi \
! -path manual/texinfo.tex ! -path scripts/config.guess \
! -path scripts/config.sub ! -path scripts/install-sh \
! -path scripts/mkinstalldirs ! -path scripts/move-if-change \
! -path INSTALL ! -path locale/programs/charmap-kw.h \
! -path po/libc.pot ! -path sysdeps/gnu/errlist.c \
! '(' -name configure \
-execdir test -f configure.ac -o -f configure.in ';' ')' \
! '(' -name preconfigure \
-execdir test -f preconfigure.ac ';' ')' \
-print)
and then by running 'make dist-prepare' to regenerate files built
from the altered files, and then executing the following to cleanup:
chmod a+x sysdeps/unix/sysv/linux/riscv/configure
# Omit irrelevant whitespace and comment-only changes,
# perhaps from a slightly-different Autoconf version.
git checkout -f \
sysdeps/csky/configure \
sysdeps/hppa/configure \
sysdeps/riscv/configure \
sysdeps/unix/sysv/linux/csky/configure
# Omit changes that caused a pre-commit check to fail like this:
# remote: *** error: sysdeps/powerpc/powerpc64/ppc-mcount.S: trailing lines
git checkout -f \
sysdeps/powerpc/powerpc64/ppc-mcount.S \
sysdeps/unix/sysv/linux/s390/s390-64/syscall.S
# Omit change that caused a pre-commit check to fail like this:
# remote: *** error: sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S: last line does not end in newline
git checkout -f sysdeps/sparc/sparc64/multiarch/memcpy-ultra3.S
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* All files with FSF copyright notices: Update copyright dates
using scripts/update-copyrights.
* locale/programs/charmap-kw.h: Regenerated.
* locale/programs/locfile-kw.h: Likewise.
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This patch makes Python 3.4 or later a required tool for building
glibc, so allowing changes of awk, perl etc. code used in the build
and test to Python code without any such changes needing makefile
conditionals or to handle older Python versions.
This patch makes the configure test for Python check the version and
give an error if Python is missing or too old, and removes makefile
conditionals that are no longer needed. It does not itself convert
any code from another language to Python, and does not remove any
compatibility with older Python versions from existing scripts.
Tested for x86_64.
* configure.ac (PYTHON_PROG): Use AC_CHECK_PROG_VER. Set
critic_missing for versions before 3.4.
* configure: Regenerated.
* manual/install.texi (Tools for Compilation): Document
requirement for Python to build glibc.
* INSTALL: Regenerated.
* Rules [PYTHON]: Make code unconditional.
* benchtests/Makefile [PYTHON]: Likewise.
* conform/Makefile [PYTHON]: Likewise.
* manual/Makefile [PYTHON]: Likewise.
* math/Makefile [PYTHON]: Likewise.
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This patch extends gen-libm-test.py to generate the ulps table for the
manual, so meaning there is only a single ulps file parser needed and
another Perl script is eliminated. As with the introduction of
gen-libm-test.py, this is designed to generate exactly the same
libm-err.texi as libm-err-tab.pl did. (gen-libm-test.py is still
shorter in lines than the old gen-libm-test.pl even after this patch.)
Note that this introduces a Python dependency for building the manual,
which is thus noted in install.texi and NEWS.
Tested building html / info / pdf versions of the manual.
* math/gen-libm-test.py: Import os.
(ALL_FLOATS_MANUAL): New constant.
(ALL_FLOATS_SUFFIX): Likewise.
(Ulps.all_functions): New function.
(real_all_ulps): Likewise.
(generate_err_table_sub): Likewise.
(generate_err_table): Likewise.
(main): Handle -s and -m options.
* manual/libm-err-tab.pl: Remove.
* manual/Makefile ($(objpfx)stamp-libm-err): Use gen-libm-test.py
instead of libm-err-tab.pl.
[$(PERL) != no]: Change condition to [$(if $(PYTHON),$(PERL),no)
!= no].
* manual/install.texi (Tools for Compilation): Document
requirement for Python to build manual.
* INSTALL: Regenerated.
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* All files with FSF copyright notices: Update copyright dates
using scripts/update-copyrights.
* locale/programs/charmap-kw.h: Regenerated.
* locale/programs/locfile-kw.h: Likewise.
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glibc has an add-ons mechanism to allow additional software to be
integrated into the glibc build. Such add-ons may be within the glibc
source tree, or outside it at a path passed to the --enable-add-ons
configure option.
localedata and crypt were once add-ons, distributed in separate
release tarballs, but long since stopped using that mechanism.
Linuxthreads was always an add-on. Ports spent some time as an add-on
with separate release tarballs, then was first moved into the glibc
source tree, then had its sysdeps files moved into the main sysdeps
hierarchy so the add-ons mechanism was no longer used. NPTL spent
some time as an add-on in the main glibc tree before stopping using
the add-on mechanism. libidn used to have separate release tarballs
but no longer does so, but still uses the add-ons mechanism within the
glibc source tree. Various other software has supported building with
the add-ons mechanism at times in the past, but I don't think any is
still widely used.
Add-ons involve significant, little-used complexity in the glibc build
system, and make it hard to understand what the space of possible
glibc configurations is. This patch removes the add-ons mechanism.
libidn is now built via the Subdirs mechanism to cause any
configuration using sysdeps/unix/inet to build libidn; HAVE_LIBIDN
(which effectively means shared libraries are available) is now
defined via sysdeps/unix/inet/configure. Various references to
add-ons around the source tree are removed (in the case of maint.texi,
the example list of sysdeps directories is still very out of date).
Externally maintained ports should now put their files in the normal
sysdeps directory structure rather than being arranged as add-ons;
they probably need to change e.g. elf.h anyway, rather than actually
being able to work just as a drop-in subtree. Hurd libpthread should
be arranged similarly to NPTL, so some files might go in a
hurd-pthreads (or similar) top-level directory in glibc, while sysdeps
files should go in the normal sysdeps directory structure (possibly in
hurd or hurd-pthreads subdirectories, just as there are nptl
subdirectories in the sysdeps tree).
Tested for x86_64, and with build-many-glibcs.py.
* configure.ac (--enable-add-ons): Remove option.
(machine): Do not mention add-ons in comment.
(LIBC_PRECONFIGURE): Likewise.
(add_ons): Remove variable and sanity checks and logic to locate
add-ons.
(add_ons_automatic): Remove variable.
(configured_add_ons): Likewise.
(add_ons_sfx): Likewise.
(add_ons_pfx): Likewise.
(add_on_subdirs): Likewise.
(sysnames_add_ons): Likewise. Remove loop over add-ons and
consideration of add-ons in Implies handling.
(sysdeps_add_ons): Likewise.
* configure: Regenerated.
* libidn/configure.ac: Remove.
* libidn/configure: Likewise.
* sysdeps/unix/inet/configure.ac: New file.
* sysdeps/unix/inet/configure: New generated file.
* sysdeps/unix/inet/Subdirs: Add libidn.
* Makeconfig (sysdeps-srcdirs): Remove variable.
(+sysdep_dirs): Do not include $(sysdeps-srcdirs).
($(common-objpfx)config.status): Do not depend on add-on files.
($(common-objpfx)shlib-versions.v.i): Do not mention add-ons in
comment.
(all-subdirs): Do not include $(add-on-subdirs).
* Makefile (dist-prepare): Do not use $(sysdeps-add-ons).
* config.make.in (add-ons): Remove variable.
(add-on-subdirs): Likewise.
(sysdeps-add-ons): Likewise.
* manual/Makefile (add-chapters): Remove.
($(objpfx)texis): Do not depend on $(add-chapters).
(nonexamples): Do not handle $(add-chapters).
(examples): Do not handle $(add-ons).
(chapters.% top-menu.%): Do not pass '$(add-chapters)' to
libc-texinfo.sh.
* manual/install.texi (Installation): Do not mention add-ons.
(--enable-add-ons): Do not document configure option.
* INSTALL: Regenerated.
* manual/libc-texinfo.sh: Do not handle $2 add-ons argument.
* manual/maint.texi (Hierarchy Conventions): Do not mention
add-ons.
* scripts/build-many-glibcs.py (Glibc.build_glibc): Do not use
--enable-add-ons.
* scripts/gen-sorted.awk: Do not handle Subdirs files from
add-ons.
* scripts/test-installation.pl: Do not handle glibc-compat add-on.
* sysdeps/nptl/Makeconfig: Do not mention add-ons in comment.
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The Summary is now generated from @standards, and syntax-checking is
performed. If invalid @standards syntax is detected, summary.pl will
fail, reporting all errors. Failure and error reporting is disabled
for now, however, since much of the manual is still incomplete
wrt. header and standards annotations.
Note that the sorting order of the Summary has changed; summary.pl
respects the locale, like summary.awk did, but the use of LC_ALL=C is
introduced in the Makefile. Other notable deviations are improved
detection of the annotated elements' names, which are used for
sorting, and improved detection of the @node used to reference into
the manual. The most noticeable difference in the rendered Summary is
that entries may now contain multiple lines, one for each header and
standard combination.
summary.pl accepts a `--help' option, which details the expected
syntax of @standards. If errors are reported, the user is directed to
this feature for further information.
* manual/Makefile: Generate summary.texi with summary.pl.
Force use of the C locale. Update Perl dependency comment.
* manual/header.texi: Update reference to summary.awk.
* manual/macros.texi: Refer authors to `summary.pl --help'.
* manual/summary.awk: Remove file.
* manual/summary.pl: New file. Generate summary.texi, and
check for @standards-related syntax errors.
* manual/argp.texi: Convert header and standards @comments to
@standards.
* manual/arith.texi: Likewise.
* manual/charset.texi: Likewise.
* manual/conf.texi: Likewise.
* manual/creature.texi: Likewise.
* manual/crypt.texi: Likewise.
* manual/ctype.texi: Likewise.
* manual/debug.texi: Likewise.
* manual/errno.texi: Likewise.
* manual/filesys.texi: Likewise.
* manual/getopt.texi: Likewise.
* manual/job.texi: Likewise.
* manual/lang.texi: Likewise.
* manual/llio.texi: Likewise.
* manual/locale.texi: Likewise.
* manual/math.texi: Likewise.
* manual/memory.texi: Likewise.
* manual/message.texi: Likewise.
* manual/pattern.texi: Likewise.
* manual/pipe.texi: Likewise.
* manual/process.texi: Likewise.
* manual/resource.texi: Likewise.
* manual/search.texi: Likewise.
* manual/setjmp.texi: Likewise.
* manual/signal.texi: Likewise.
* manual/socket.texi: Likewise.
* manual/startup.texi: Likewise.
* manual/stdio.texi: Likewise.
* manual/string.texi: Likewise.
* manual/sysinfo.texi: Likewise.
* manual/syslog.texi: Likewise.
* manual/terminal.texi: Likewise.
* manual/threads.texi: Likewise.
* manual/time.texi: Likewise.
* manual/users.texi: Likewise.
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Create a new node for tunables documentation and add notes for the
malloc tunables.
* manual/tunables.texi: New chapter.
* manual/Makefile (chapters): Add it.
* manual/probes.texi (@node): Point to the Tunables chapter.
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Do not try to generate the manual when perl is unavailable. This
matches the behavior when makeinfo is unavailable. Otherwise the
install step fails when trying to generate the libm section since
it runs a perl script.
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for ChangeLog
* manual/Makefile ($(objpfx)stamp-summary): Require
check-safety.sh to pass.
* manual/check-safety.sh: Wish for verification that every
@deftypefn and @deftypefun is followed by a @safety remark.
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* manual/Makefile (INSTALL_INFO): Remove variable setting.
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In <https://sourceware.org/ml/libc-alpha/2014-01/msg00196.html> I
noted it was necessary to add includes of Makeconfig early in various
subdirectory makefiles for the tests-special variable settings added
by that patch to be conditional on configuration information. No-one
commented on the general question there of whether Makeconfig should
always be included immediately after the definition of subdir.
This patch implements that early inclusion of Makeconfig in each
directory (which is a lot easier than consistent placement of includes
of Rules). Includes are added if needed, or moved up if already
present. Subdirectory "all:" targets are removed, since Makeconfig
provides one.
There is potential for further cleanups I haven't done. Rules and
Makerules have code such as
ifneq "$(findstring env,$(origin headers))" ""
headers :=
endif
to override to empty any value of various variables that came from the
environment. I think there is a case for Makeconfig setting all the
subdirectory variables (other than subdir) to empty to ensure no
outside value is going to take effect if a subdirectory fails to
define a variable. (A list of such variables, possibly out of date
and incomplete, is in manual/maint.texi.) Rules and Makerules would
give errors if Makeconfig hadn't already been included, instead of
including it themselves. The special code to override values coming
from the environment would then be obsolete and could be removed.
Tested x86_64, including that installed binaries are identical before
and after the patch.
* argp/Makefile: Include Makeconfig immediately after defining
subdir.
* assert/Makefile: Likewise.
* benchtests/Makefile: Likewise.
* catgets/Makefile: Likewise.
* conform/Makefile: Likewise.
* crypt/Makefile: Likewise.
* csu/Makefile: Likewise.
(all): Remove target.
* ctype/Makefile: Include Makeconfig immediately after defining
subdir.
* debug/Makefile: Likewise.
* dirent/Makefile: Likewise.
* dlfcn/Makefile: Likewise.
* gmon/Makefile: Likewise.
* gnulib/Makefile: Likewise.
* grp/Makefile: Likewise.
* gshadow/Makefile: Likewise.
* hesiod/Makefile: Likewise.
* hurd/Makefile: Likewise.
(all): Remove target.
* iconvdata/Makefile: Include Makeconfig immediately after
defining subdir.
* inet/Makefile: Likewise.
* intl/Makefile: Likewise.
* io/Makefile: Likewise.
* libio/Makefile: Likewise.
(all): Remove target.
* locale/Makefile: Include Makeconfig immediately after defining
subdir.
* login/Makefile: Likewise.
* mach/Makefile: Likewise.
(all): Remove target.
* malloc/Makefile: Include Makeconfig immediately after defining
subdir.
(all): Remove target.
* manual/Makefile: Include Makeconfig immediately after defining
subdir.
* math/Makefile: Likewise.
* misc/Makefile: Likewise.
* nis/Makefile: Likewise.
* nss/Makefile: Likewise.
* po/Makefile: Likewise.
(all): Remove target.
* posix/Makefile: Include Makeconfig immediately after defining
subdir.
* pwd/Makefile: Likewise.
* resolv/Makefile: Likewise.
* resource/Makefile: Likewise.
* rt/Makefile: Likewise.
* setjmp/Makefile: Likewise.
* shadow/Makefile: Likewise.
* signal/Makefile: Likewise.
* socket/Makefile: Likewise.
* soft-fp/Makefile: Likewise.
* stdio-common/Makefile: Likewise.
* stdlib/Makefile: Likewise.
* streams/Makefile: Likewise.
* string/Makefile: Likewise.
* sunrpc/Makefile: Likewise.
(all): Remove target.
* sysvipc/Makefile: Include Makeconfig immediately after defining
subdir.
* termios/Makefile: Likewise.
* time/Makefile: Likewise.
* timezone/Makefile: Likewise.
(all): Remove target.
* wcsmbs/Makefile: Include Makeconfig immediately after defining
subdir.
* wctype/Makefile: Likewise.
libidn/ChangeLog:
* Makefile: Include Makeconfig immediately after defining subdir.
localedata/ChangeLog:
* Makefile: Include Makeconfig immediately after defining subdir.
(all): Remove target.
nptl/ChangeLog:
* Makefile: Include Makeconfig immediately after defining subdir.
nptl_db/ChangeLog:
* Makefile: Include Makeconfig immediately after defining subdir.
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This patch adds a new "Inter-Process Communication"
chapter to cover the sem*, msg*, and shm* functions.
Initially we document only the sem* function signatures
and their safety notes.
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* manual/Makefile ($(objpfx)stamp-summary): Run it.
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for ChangeLog
* malloc/malloc.c: Include stap-probe.h.
(__libc_mallopt): Add memory_mallopt probe.
* malloc/arena.c (_int_new_arena): Add memory_arena_new probe.
* manual/probes.texi: New.
* manual/Makefile (chapters): Add probes.
* manual/threads.texi: Set next node.
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The manual and its file names are about interfaces and not the
implementation details.
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This adds the base chapter for POSIX threads and also documentation
for thread-specific data, along with a note on its interaction with
C++11 thread_local variables.
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