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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the pown functions, which are like pow but with an
integer exponent. That exponent has type long long int in C23; it was
intmax_t in TS 18661-4, and as with other interfaces changed after
their initial appearance in the TS, I don't think we need to support
the original version of the interface. The test inputs are based on
the subset of test inputs for pow that use integer exponents that fit
in long long.
As the first such template implementation that saves and restores the
rounding mode internally (to avoid possible issues with directed
rounding and intermediate overflows or underflows in the wrong
rounding mode), support also needed to be added for using
SET_RESTORE_ROUND* in such template function implementations. This
required math-type-macros-float128.h to include <fenv_private.h>, so
it can tell whether SET_RESTORE_ROUNDF128 is defined. In turn, the
include order with <fenv_private.h> included before <math_private.h>
broke loongarch builds, showing up that
sysdeps/loongarch/math_private.h is really a fenv_private.h file
(maybe implemented internally before the consistent split of those
headers in 2018?) and needed to be renamed to fenv_private.h to avoid
errors with duplicate macro definitions if <math_private.h> is
included after <fenv_private.h>.
The underlying implementation uses __ieee754_pow functions (called
more than once in some cases, where the exponent does not fit in the
floating type). I expect a custom implementation for a given format,
that only handles integer exponents but handles larger exponents
directly, could be faster and more accurate in some cases.
I encourage searching for worst cases for ulps error for these
implementations (necessarily non-exhaustively, given the size of the
input space).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the powr functions, which are like pow, but with simpler
handling of special cases (based on exp(y*log(x)), so negative x and
0^0 are domain errors, powers of -0 are always +0 or +Inf never -0 or
-Inf, and 1^+-Inf and Inf^0 are also domain errors, while NaN^0 and
1^NaN are NaN). The test inputs are taken from those for pow, with
appropriate adjustments (including removing all tests that would be
domain errors from those in auto-libm-test-in and adding some more
such tests in libm-test-powr.inc).
The underlying implementation uses __ieee754_pow functions after
dealing with all special cases that need to be handled differently.
It might be a little faster (avoiding a wrapper and redundant checks
for special cases) to have an underlying implementation built
separately for both pow and powr with compile-time conditionals for
special-case handling, but I expect the benefit of that would be
limited given that both functions will end up needing to use the same
logic for computing pow outside of special cases.
My understanding is that powr(negative, qNaN) should raise "invalid":
that the rule on "invalid" for an argument outside the domain of the
function takes precedence over a quiet NaN argument producing a quiet
NaN result with no exceptions raised (for rootn it's explicit that the
0th root of qNaN raises "invalid"). I've raised this on the WG14
reflector to confirm the intent.
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the rsqrt functions (1/sqrt(x)). The test inputs are
taken from those for sqrt.
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the atan2pi functions (atan2(y,x)/pi).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the atanpi functions (atan(x)/pi).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the asinpi functions (asin(x)/pi).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the acospi functions (acos(x)/pi).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the tanpi functions (tan(pi*x)).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the sinpi functions (sin(pi*x)).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the cospi functions (cos(pi*x)).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the exp2m1 and exp10m1 functions (exp2(x)-1 and
exp10(x)-1, like expm1).
As with other such functions, these use type-generic templates that
could be replaced with faster and more accurate type-specific
implementations in future. Test inputs are copied from those for
expm1, plus some additions close to the overflow threshold (copied
from exp2 and exp10) and also some near the underflow threshold.
exp2m1 has the unusual property of having an input (M_MAX_EXP) where
whether the function overflows (under IEEE semantics) depends on the
rounding mode. Although these could reasonably be XFAILed in the
testsuite (as we do in some cases for arguments very close to a
function's overflow threshold when an error of a few ulps in the
implementation can result in the implementation not agreeing with an
ideal one on whether overflow takes place - the testsuite isn't smart
enough to handle this automatically), since these functions aren't
required to be correctly rounding, I made the implementation check for
and handle this case specially.
The Makefile ordering expected by lint-makefiles for the new functions
is a bit peculiar, but I implemented it in this patch so that the test
passes; I don't know why log2 also needed moving in one Makefile
variable setting when it didn't in my previous patches, but the
failure showed a different place was expected for that function as
well.
The powerpc64le IFUNC setup seems not to be as self-contained as one
might hope; it shouldn't be necessary to add IFUNCs for new functions
such as these simply to get them building, but without setting up
IFUNCs for the new functions, there were undefined references to
__GI___expm1f128 (that IFUNC machinery results in no such function
being defined, but doesn't stop include/math.h from doing the
redirection resulting in the exp2m1f128 and exp10m1f128
implementations expecting to call it).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the log10p1 functions (log10(1+x): like log1p, but for
base-10 logarithms).
This is directly analogous to the log2p1 implementation (except that
whereas log2p1 has a smaller underflow range than log1p, log10p1 has a
larger underflow range). The test inputs are copied from those for
log1p and log2p1, plus a few more inputs in that wider underflow
range.
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the logp1 functions (aliases for log1p functions - the
name is intended to be more consistent with the new log2p1 and
log10p1, where clearly it would have been very confusing to name those
functions log21p and log101p). As aliases rather than new functions,
the content of this patch is somewhat different from those actually
adding new functions.
Tests are shared with log1p, so this patch *does* mechanically update
all affected libm-test-ulps files to expect the same errors for both
functions.
The vector versions of log1p on aarch64 and x86_64 are *not* updated
to have logp1 aliases (and thus there are no corresponding header,
tests, abilist or ulps changes for vector functions either). It would
be reasonable for such vector aliases and corresponding changes to
other files to be made separately. For now, the log1p tests instead
avoid testing logp1 in the vector case (a Makefile change is needed to
avoid problems with grep, used in generating the .c files for vector
function tests, matching more than one ALL_RM_TEST line in a file
testing multiple functions with the same inputs, when it assumes that
the .inc file only has a single such line).
Tested for x86_64 and x86, and with build-many-glibcs.py.
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C23 adds various <math.h> function families originally defined in TS
18661-4. Add the log2p1 functions (log2(1+x): like log1p, but for
base-2 logarithms).
This illustrates the intended structure of implementations of all
these function families: define them initially with a type-generic
template implementation. If someone wishes to add type-specific
implementations, it is likely such implementations can be both faster
and more accurate than the type-generic one and can then override it
for types for which they are implemented (adding benchmarks would be
desirable in such cases to demonstrate that a new implementation is
indeed faster).
The test inputs are copied from those for log1p. Note that these
changes make gen-auto-libm-tests depend on MPFR 4.2 (or later).
The bulk of the changes are fairly generic for any such new function.
(sysdeps/powerpc/nofpu/Makefile only needs changing for those
type-generic templates that use fabs.)
Tested for x86_64 and x86, and with build-many-glibcs.py.
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WG14 decided to use the name C23 as the informal name of the next
revision of the C standard (notwithstanding the publication date in
2024). Update references to C2X in glibc to use the C23 name.
This is intended to update everything *except* where it involves
renaming files (the changes involving renaming tests are intended to
be done separately). In the case of the _ISOC2X_SOURCE feature test
macro - the only user-visible interface involved - support for that
macro is kept for backwards compatibility, while adding
_ISOC23_SOURCE.
Tested for x86_64.
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<tgmath.h> implements semantics for integer generic arguments that
handle cases involving _FloatN / _FloatNx types as specified in TS
18661-3 plus some defect fixes.
C2x has further changes to the semantics for <tgmath.h> macros with
such types, which should also be considered defect fixes (although
handled through the integration of TS 18661-3 in C2x rather than
through an issue tracking process). Specifically, the rules were
changed because of problems raised with using the macros with the
evaluation format types such as float_t and _Float32_t: the older
version of the rules didn't allow passing _FloatN / _FloatNx types to
the narrowing macros returning float or double, or passing float /
double / long double to the narrowing macros returning _FloatN /
_FloatNx, which was a problem with the evaluation format types which
could be either kind of type depending on the value of
FLT_EVAL_METHOD.
Thus the new rules allow cases of mixing types which were not allowed
before, and, as part of the changes, the handling of integer arguments
was also changed: if there is any _FloatNx generic argument, integer
generic arguments are treated as _Float32x (not double), while the
rule about treating integer arguments to narrowing macros returning
_FloatN or _FloatNx as _Float64 not double was removed (no longer
needed now double is a valid argument to such macros).
I've implemented the changes in GCC's __builtin_tgmath, which thus
requires updates to glibc's test expectations so that the tests
continue to build with GCC 13 (the test is also updated to test the
argument types that weren't allowed before but are now valid under C2x
rules).
Given those test changes, it's then also necessary to fix the
implementations in <tgmath.h> to have appropriate semantics with older
GCC so that the tests pass with GCC versions before GCC 13 as well.
For some cases (non-narrowing macros with two or three generic
arguments; narrowing macros returning _Float32x), the older version of
__builtin_tgmath doesn't correspond sufficiently well to C2x
semantics, so in those cases <tgmath.h> is adjusted to use the older
macro implementation instead of __builtin_tgmath. The older macro
implementation is itself adjusted to give the desired semantics, with
GCC 7 and later. (It's not possible to get the right semantics in all
cases for the narrowing macros with GCC 6 and before when the _FloatN
/ _FloatNx names are typedefs rather than distinct types.)
Tested as follows: with the full glibc testsuite for x86_64, GCC 6, 7,
11, 13; with execution of the math/tests for aarch64, arm, powerpc and
powerpc64le, GCC 6, 7, 12 and 13 (powerpc64le only with GCC 12 and
13); with build-many-glibcs.py with GCC 6, 7, 12 and 13.
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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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glibc has had exp10 functions since long before they were
standardized; now they are standardized in TS 18661-4 and C2X, they
are also specified there to have a corresponding type-generic macro.
Add one to <tgmath.h>, so fixing bug 26108.
glibc doesn't have other functions from TS 18661-4 yet, but when
added, it will be natural to add the type-generic macro for each
function family at the same time as the functions.
Tested for x86_64.
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At the last WG14 meeting,
<http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2711.htm> was
accepted, which places more emphasis on the new fmaximum / fminimum
functions and less on the old fmax / fmin functions. Some of the
changes are to examples, notes or otherwise don't require
implementation changes. However, the changes include removing the
_FloatN / _FloatNx versions of the fmax and fmin functions that came
from TS 18661-3.
Thus, those function versions should only be declared under similar
conditions to the _FloatN / _FloatNx versions of fmaxmag and fminmag:
for _GNU_SOURCE and pre-C2X use of __STDC_WANT_IEC_60559_TYPES_EXT__,
but not for C2X without _GNU_SOURCE.
In turn this requires a tgmath.h change so that the corresponding
tgmath.h macros, for C2X with __STDC_WANT_IEC_60559_TYPES_EXT__ but
without _GNU_SOURCE, don't try to use function variants that aren't
declared. (That issue doesn't arise for the tgmath.h macros for
fmaxmag and fminmag, because those aren't defined at all in those
circumstances unless __STDC_WANT_IEC_60559_BFP_EXT__ (from TS 18661-1
and not specified at all by C2X) is also defined, and in that case the
_FloatN / _FloatNx versions of fmaxmag and fminmag get declared - this
is only ever an issue when it's possible for some functions
corresponding to a type-generic-macro to be declared, and for _FloatN
/ _FloatNx functions in general to be declared, but without the
_FloatN / _FloatNx functions corresponding to that particular macro
being declared.)
Tested for x86_64.
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C2X does not include fmaxmag and fminmag. When I updated feature test
macro handling accordingly (commit
858045ad1c5ac1682288bbcb3676632b97a21ddf, "Update floating-point
feature test macro handling for C2X", included in 2.34), I missed
updating tgmath.h so it doesn't define the corresponding type-generic
macros unless __STDC_WANT_IEC_60559_BFP_EXT__ is defined; I've now
reported this as bug 28397. Adjust the conditionals in tgmath.h
accordingly.
Tested for x86_64.
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C2X adds new <math.h> functions for floating-point maximum and
minimum, corresponding to the new operations that were added in IEEE
754-2019 because of concerns about the old operations not being
associative in the presence of signaling NaNs. fmaximum and fminimum
handle NaNs like most <math.h> functions (any NaN argument means the
result is a quiet NaN). fmaximum_num and fminimum_num handle both
quiet and signaling NaNs the way fmax and fmin handle quiet NaNs (if
one argument is a number and the other is a NaN, return the number),
but still raise "invalid" for a signaling NaN argument, making them
exceptions to the normal rule that a function with a floating-point
result raising "invalid" also returns a quiet NaN. fmaximum_mag,
fminimum_mag, fmaximum_mag_num and fminimum_mag_num are corresponding
functions returning the argument with greatest or least absolute
value. All these functions also treat +0 as greater than -0. There
are also corresponding <tgmath.h> type-generic macros.
Add these functions to glibc. The implementations use type-generic
templates based on those for fmax, fmin, fmaxmag and fminmag, and test
inputs are based on those for those functions with appropriate
adjustments to the expected results. The RISC-V maintainers might
wish to add optimized versions of fmaximum_num and fminimum_num (for
float and double), since RISC-V (F extension version 2.2 and later)
provides instructions corresponding to those functions - though it
might be at least as useful to add architecture-independent built-in
functions to GCC and teach the RISC-V back end to expand those
functions inline, which is what you generally want for functions that
can be implemented with a single instruction.
Tested for x86_64 and x86, and with build-many-glibcs.py.
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This patch adds the narrowing fused multiply-add functions from TS
18661-1 / TS 18661-3 / C2X to glibc's libm: ffma, ffmal, dfmal,
f32fmaf64, f32fmaf32x, f32xfmaf64 for all configurations; f32fmaf64x,
f32fmaf128, f64fmaf64x, f64fmaf128, f32xfmaf64x, f32xfmaf128,
f64xfmaf128 for configurations with _Float64x and _Float128;
__f32fmaieee128 and __f64fmaieee128 aliases in the powerpc64le case
(for calls to ffmal and dfmal when long double is IEEE binary128).
Corresponding tgmath.h macro support is also added.
The changes are mostly similar to those for the other narrowing
functions previously added, especially that for sqrt, so the
description of those generally applies to this patch as well. As with
sqrt, I reused the same test inputs in auto-libm-test-in as for
non-narrowing fma rather than adding extra or separate inputs for
narrowing fma. The tests in libm-test-narrow-fma.inc also follow
those for non-narrowing fma.
The non-narrowing fma has a known bug (bug 6801) that it does not set
errno on errors (overflow, underflow, Inf * 0, Inf - Inf). Rather
than fixing this or having narrowing fma check for errors when
non-narrowing does not (complicating the cases when narrowing fma can
otherwise be an alias for a non-narrowing function), this patch does
not attempt to check for errors from narrowing fma and set errno; the
CHECK_NARROW_FMA macro is still present, but as a placeholder that
does nothing, and this missing errno setting is considered to be
covered by the existing bug rather than needing a separate open bug.
missing-errno annotations are duly added to many of the
auto-libm-test-in test inputs for fma.
This completes adding all the new functions from TS 18661-1 to glibc,
so will be followed by corresponding stdc-predef.h changes to define
__STDC_IEC_60559_BFP__ and __STDC_IEC_60559_COMPLEX__, as the support
for TS 18661-1 will be at a similar level to that for C standard
floating-point facilities up to C11 (pragmas not implemented, but
library functions done). (There are still further changes to be done
to implement changes to the types of fromfp functions from N2548.)
Tested as followed: natively with the full glibc testsuite for x86_64
(GCC 11, 7, 6) and x86 (GCC 11); with build-many-glibcs.py with GCC
11, 7 and 6; cross testing of math/ tests for powerpc64le, powerpc32
hard float, mips64 (all three ABIs, both hard and soft float). The
different GCC versions are to cover the different cases in tgmath.h
and tgmath.h tests properly (GCC 6 has _Float* only as typedefs in
glibc headers, GCC 7 has proper _Float* support, GCC 8 adds
__builtin_tgmath).
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This patch adds the narrowing square root functions from TS 18661-1 /
TS 18661-3 / C2X to glibc's libm: fsqrt, fsqrtl, dsqrtl, f32sqrtf64,
f32sqrtf32x, f32xsqrtf64 for all configurations; f32sqrtf64x,
f32sqrtf128, f64sqrtf64x, f64sqrtf128, f32xsqrtf64x, f32xsqrtf128,
f64xsqrtf128 for configurations with _Float64x and _Float128;
__f32sqrtieee128 and __f64sqrtieee128 aliases in the powerpc64le case
(for calls to fsqrtl and dsqrtl when long double is IEEE binary128).
Corresponding tgmath.h macro support is also added.
The changes are mostly similar to those for the other narrowing
functions previously added, so the description of those generally
applies to this patch as well. However, the not-actually-narrowing
cases (where the two types involved in the function have the same
floating-point format) are aliased to sqrt, sqrtl or sqrtf128 rather
than needing a separately built not-actually-narrowing function such
as was needed for add / sub / mul / div. Thus, there is no
__nldbl_dsqrtl name for ldbl-opt because no such name was needed
(whereas the other functions needed such a name since the only other
name for that entry point was e.g. f32xaddf64, not reserved by TS
18661-1); the headers are made to arrange for sqrt to be called in
that case instead.
The DIAG_* calls in sysdeps/ieee754/soft-fp/s_dsqrtl.c are because
they were observed to be needed in GCC 7 testing of
riscv32-linux-gnu-rv32imac-ilp32. The other sysdeps/ieee754/soft-fp/
files added didn't need such DIAG_* in any configuration I tested with
build-many-glibcs.py, but if they do turn out to be needed in more
files with some other configuration / GCC version, they can always be
added there.
I reused the same test inputs in auto-libm-test-in as for
non-narrowing sqrt rather than adding extra or separate inputs for
narrowing sqrt. The tests in libm-test-narrow-sqrt.inc also follow
those for non-narrowing sqrt.
Tested as followed: natively with the full glibc testsuite for x86_64
(GCC 11, 7, 6) and x86 (GCC 11); with build-many-glibcs.py with GCC
11, 7 and 6; cross testing of math/ tests for powerpc64le, powerpc32
hard float, mips64 (all three ABIs, both hard and soft float). The
different GCC versions are to cover the different cases in tgmath.h
and tgmath.h tests properly (GCC 6 has _Float* only as typedefs in
glibc headers, GCC 7 has proper _Float* support, GCC 8 adds
__builtin_tgmath).
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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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When adding some of the TS 18661 narrowing functions for glibc 2.28, I
deferred adding corresponding <tgmath.h> support because of unresolved
questions about the specification for those type-generic macros,
especially in relation to _FloatN and _FloatNx types.
Those issues are now clarified in the response to Clarification
Request 13 to TS 18661-3, and this patch adds the deferred tgmath.h
support. As with other tgmath.h macros, there are fairly
straightforward implementations based on __builtin_tgmath for GCC 8
and later, which result in exactly the right function being called in
each case, and more complicated implementations for GCC 7 and earlier,
which generally result in a function being called whose arguments have
the right format (i.e. an alias for the right function), but which
might not be exactly the function name specified by TS 18661.
In one case with older compilers (f32x* macros, where the type
_Float64x exists and all the arguments have type _Float32 or
_Float32x), there is a further relaxation and the function called may
have arguments narrower than the one specified by the TS, but still
wide enough to represent the arguments exactly, so the result of the
call is unchanged (as this does not affect any case where rounding of
integer arguments might be involved). With GCC 6 or before this is
inherently unavoidable (but still harmless and not detectable by how
the compiled program behaves, unless it redefines the functions in
question like the testcases do) because _Float32x and _Float64 are
both typedefs for double in that case but the specified semantics
result in different functions, with different argument formats, being
called for those two argument types.
Tests for the new macros are handled through gen-tgmath-tests.py,
which deals with the special-case handling for older GCC.
Tested as follows: with the full glibc testsuite on x86_64 and x86
(with GCC 6, 7 and 8); with the math/ tests on aarch64 and arm (with
GCC 6, 7 and 8); with build-many-glibcs.py (with GCC 6, 7 and 9).
* math/tgmath.h [__HAVE_FLOAT128X]: Give error.
[(__HAVE_FLOAT64X && !__HAVE_FLOAT128)
|| (__HAVE_FLOAT128 && !__HAVE_FLOAT64X)]: Likewise.
(__TGMATH_2_NARROW_F): Likewise.
(__TGMATH_2_NARROW_D): New macro.
(__TGMATH_2_NARROW_F16): Likewise.
(__TGMATH_2_NARROW_F32): Likewise.
(__TGMATH_2_NARROW_F64): Likewise.
(__TGMATH_2_NARROW_F32X): Likewise.
(__TGMATH_2_NARROW_F64X): Likewise.
[__HAVE_BUILTIN_TGMATH] (__TGMATH_NARROW_FUNCS_F): Likewise.
[__HAVE_BUILTIN_TGMATH] (__TGMATH_NARROW_FUNCS_F16): Likewise.
[__HAVE_BUILTIN_TGMATH] (__TGMATH_NARROW_FUNCS_F32): Likewise.
[__HAVE_BUILTIN_TGMATH] (__TGMATH_NARROW_FUNCS_F64): Likewise.
[__HAVE_BUILTIN_TGMATH] (__TGMATH_NARROW_FUNCS_F32X): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (fadd): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (dadd): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (fdiv): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (ddiv): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (fmul): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (dmul): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (fsub): Likewise.
[__GLIBC_USE (IEC_60559_BFP_EXT_C2X)] (dsub): Likewise.
[__GLIBC_USE (IEC_60559_TYPES_EXT) && __HAVE_FLOAT16] (f16add):
Likewise.
[__GLIBC_USE (IEC_60559_TYPES_EXT) && __HAVE_FLOAT16] (f16div):
Likewise.
[__GLIBC_USE (IEC_60559_TYPES_EXT) && __HAVE_FLOAT16] (f16mul):
Likewise.
[__GLIBC_USE (IEC_60559_TYPES_EXT) &a |
