Continuing the fixes for C90 libm functions calling C99 fe* functions,
this patch fixes the case of fegetround by making it a weak alias of
__fegetround and making the affected code call __fegetround.
Tested for x86_64 (testsuite, and that disassembly of installed shared
libraries is unchanged by the patch). Also tested for ARM
(soft-float) that fegetround failures disappear from the linknamespace
test failures (feholdexcept, fesetenv, fesetround and feupdateenv
remain to be addressed before bug 17748 is fully fixed, although this
patch may suffice to fix the failures in some cases, when the libc_fe*
functions are implemented but there is no architecture-specific sqrt
implementation in use so there were failures from fegetround used by
sqrt but no other such failures).
[BZ #17748]
* include/fenv.h (__fegetround): Declare. Use libm_hidden_proto.
* math/fegetround.c (fegetround): Rename to __fegetround and
define as weak alias of __fegetround. Use libm_hidden_weak.
* sysdeps/aarch64/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/alpha/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/arm/fegetround.c (fegetround): Likewise.
* sysdeps/hppa/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/i386/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/ia64/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/m68k/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/mips/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/powerpc/fpu/fegetround.c (fegetround): Likewise.
Undefine after rather than before function definition; use
parentheses around function name in definition.
(__fegetround): Also undefine macro after function definition.
* sysdeps/powerpc/nofpu/fegetround.c (fegetround): Rename to
__fegetround and define as weak alias of __fegetround. Use
libm_hidden_weak. Do not undefine as macro.
* sysdeps/powerpc/powerpc32/e500/nofpu/fegetround.c (fegetround):
Likewise.
* sysdeps/s390/fpu/fegetround.c (fegetround): Rename to
__fegetround and define as weak alias of __fegetround. Use
libm_hidden_weak.
* sysdeps/sh/sh4/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/sparc/fpu/fegetround.c (fegetround): Likewise.
* sysdeps/tile/math_private.h (__fegetround): New inline function.
* sysdeps/x86_64/fpu/fegetround.c (fegetround): Rename to
__fegetround and define as weak alias of __fegetround. Use
libm_hidden_weak.
* sysdeps/ieee754/dbl-64/e_sqrt.c (__ieee754_sqrt): Use
__fegetround instead of fegetround.
Some C90 libm functions call fegetenv via libc_feholdsetround*
functions in math_private.h. This patch makes them call __fegetenv
instead, making fegetenv into a weak alias for __fegetenv as needed.
Tested for x86_64 (testsuite, and that disassembly of installed shared
libraries is unchanged by the patch). Also tested for ARM
(soft-float) that fegetenv failures disappear from the linknamespace
test failures (however, similar fixes will also be needed for
fegetround, feholdexcept, fesetenv, fesetround and feupdateenv before
this set of namespace issues covered by bug 17748 is fully fixed and
those linknamespace tests start passing).
[BZ #17748]
* include/fenv.h (__fegetenv): Use libm_hidden_proto.
* math/fegetenv.c (__fegetenv): Use libm_hidden_def.
* sysdeps/aarch64/fpu/fegetenv.c (fegetenv): Rename to __fegetenv
and define as weak alias of __fegetenv. Use libm_hidden_weak.
* sysdeps/alpha/fpu/fegetenv.c (__fegetenv): Use libm_hidden_def.
* sysdeps/arm/fegetenv.c (fegetenv): Rename to __fegetenv and
define as weak alias of __fegetenv. Use libm_hidden_weak.
* sysdeps/hppa/fpu/fegetenv.c (fegetenv): Likewise.
* sysdeps/i386/fpu/fegetenv.c (__fegetenv): Use libm_hidden_def.
* sysdeps/ia64/fpu/fegetenv.c (fegetenv): Rename to __fegetenv and
define as weak alias of __fegetenv. Use libm_hidden_weak.
* sysdeps/m68k/fpu/fegetenv.c (__fegetenv): Use libm_hidden_def.
* sysdeps/mips/fpu/fegetenv.c (fegetenv): Rename to __fegetenv and
define as weak alias of __fegetenv. Use libm_hidden_weak.
* sysdeps/powerpc/fpu/fegetenv.c (__fegetenv): Use
libm_hidden_def.
* sysdeps/powerpc/nofpu/fegetenv.c (__fegetenv): Likewise.
* sysdeps/powerpc/powerpc32/e500/nofpu/fegetenv.c (__fegetenv):
Likewise.
* sysdeps/s390/fpu/fegetenv.c (fegetenv): Rename to __fegetenv and
define as weak alias of __fegetenv. Use libm_hidden_weak.
* sysdeps/sh/sh4/fpu/fegetenv.c (fegetenv): Likewise.
* sysdeps/sparc/fpu/fegetenv.c (__fegetenv): Use libm_hidden_def.
* sysdeps/tile/math_private.h (__fegetenv): New inline function.
* sysdeps/x86_64/fpu/fegetenv.c (fegetenv): Rename to __fegetenv
and define as weak alias of __fegetenv. Use libm_hidden_weak.
* sysdeps/generic/math_private.h (libc_feholdsetround_ctx): Use
__fegetenv instead of fegetenv.
(libc_feholdsetround_noex_ctx): Likewise.
The natural fix for some linknamespace test failures, where C90 libm
functions call C99 <fenv.h> functions, is to make fe* into weak
aliases for __fe* and call __fe* from within libm as needed.
To do this, the __fe* names need to be available for that purpose -
that is, they must not be used for something other than aliases of
fe*. On powerpc, however, __fegetround is an inline function in
fenv_libc.h, with no corresponding fegetround inline function;
fegetround has an equivalent macro expansion in bits/fenvinline.h, but
that is disabled if __NO_MATH_INLINES (which is defined for building
libm).
I see no need for that disabling; it's not even clear that
__NO_MATH_INLINES should affect <fenv.h>, and the results of
fegetround are completely defined so there is no semantic effect of
that disabling at all outside glibc. The x86 inline feraiseexcept is
conditioned on __USE_EXTERN_INLINES not __NO_MATH_INLINES (but that's
an inline function rather than a macro).
This patch removes the __NO_MATH_INLINES conditional on that
fegetround macro, so resulting in it being expanded inline inside
glibc. In turn, this means that direct calls to __fegetround from C99
functions in ldbl-128ibm can be changed to calls to fegetround, so
that nofpu fenv_libc.h files don't need to define __fegetround at all
and, by changing ldbl-128ibm files to use <fenv.h> not <fenv_libc.h>,
non-e500 nofpu no longer needs an fenv_libc.h file.
The other macros in fenvinline.h are left conditional on
__NO_MATH_INLINES, although since the only case where this should make
a difference is one involving undefined behavior (if the argument to
the function is not a valid exception macro).
The out-of-line definition for fegetround uses __fegetround (the
inline function removed by this patch). So this continues to work,
the fenvinline.h header is made to define __fegetround, and then to
define fegetround to call __fegetround.
Tested for powerpc32 (hard float) that installed stripped shared
libraries are unchanged by this patch; also tested that powerpc-nofpu
build still works. (This patch does not itself fix any bugs; it
simply cleans things up in preparation for separate bug fixes.)
* sysdeps/powerpc/bits/fenvinline.h (fegetround): Rename macro to
__fegetround and redefine to call __fegetround. Remove condition
on [!__NO_MATH_INLINES].
* sysdeps/powerpc/fpu/fenv_libc.h (__fegetround): Remove inline
function.
* sysdeps/powerpc/nofpu/fenv_libc.h: Remove file.
* sysdeps/powerpc/powerpc32/e500/nofpu/fenv_libc.h (__fegetround):
Remove macro.
* sysdeps/ieee754/ldbl-128ibm/s_llrintl.c: Include <fenv.h>
instead of <fenv_libc.h>.
(__llrintl): Call fegetround instead of __fegetround.
* sysdeps/ieee754/ldbl-128ibm/s_llroundl.c: Include <fenv.h>
instead of <fenv_libc.h>.
* sysdeps/ieee754/ldbl-128ibm/s_lrintl.c: Likewise.
(__lrintl): Call fegetround instead of __fegetround.
* sysdeps/ieee754/ldbl-128ibm/s_lroundl.c: Include <fenv.h>
instead of <fenv_libc.h>.
* sysdeps/ieee754/ldbl-128ibm/s_rintl.c: Likewise.
(__rintl): Call fegetround instead of __fegetround.
Various C90 and UNIX98 libm functions call feraiseexcept, which is not
in those standards. This causes linknamespace test failures - except
on x86 / x86_64, where feraiseexcept is inline (for the relevant
constant arguments) in bits/fenv.h.
This patch fixes this by making those functions call __feraiseexcept
instead. All changes are applied to all architectures rather than
considering the possibility that some might not be needed in some
cases (e.g. x86) as it seems most maintainable to keep architectures
consistent.
Where __feraiseexcept does not exist, it is added, with feraiseexcept
made a weak alias; where it is a strong alias, it is made weak.
libm_hidden_def / libm_hidden_proto are used with __feraiseexcept
(this might in some cases improve code generation for existing calls
to __feraiseexcept in some code on some architectures). Where there
are dummy feraiseexcept macros (on architectures without
floating-point exceptions support, to avoid compile errors from
references to undefined FE_* macros), corresponding dummy
__feraiseexcept macros are added. And on x86, to ensure
__feraiseexcept calls still get inlined, the inline function in
bits/fenv.h is refactored so that most of it can be reused in an
inline __feraiseexcept in a separate include/bits/fenv.h.
Calls are changed in C90/UNIX98 functions, but generally not in
functions missing from those standards. They are also changed in
libc_fe* functions (on the basis that those might be used in any libm
function), and in feupdateenv (on the same basis - may be used, via
default libc_*, in any libm function - of course feupdateenv will need
changing to __feupdateenv in a subsequent patch to make that fully
namespace-clean).
No __feraiseexcept is added corresponding to the feraiseexcept in
powerpc bits/fenvinline.h, because that macro definition is
conditional on !defined __NO_MATH_INLINES, and glibc libm is built
with -D__NO_MATH_INLINES, so changing internal calls to use
__feraiseexcept should make no difference.
Tested for x86_64 (testsuite; the only change in disassembly of
installed shared libraries is a slight code reordering in clog10, of
no apparent significance). Also tested for MIPS, where (in the
configuration tested) it eliminates math.h linknamespace failures for
n32 and n64 (some for o32 remain because of other issues).
[BZ #17723]
* include/fenv.h (__feraiseexcept): Use libm_hidden_proto.
* math/fraiseexcpt.c (__feraiseexcept): Use libm_hidden_def.
* sysdeps/aarch64/fpu/fraiseexcpt.c (feraiseexcept): Rename to
__feraiseexcept and define as weak alias of __feraiseexcept. Use
libm_hidden_weak.
* sysdeps/arm/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/hppa/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/i386/fpu/fraiseexcpt.c (__feraiseexcept): Use
libm_hidden_def.
* sysdeps/ia64/fpu/fraiseexcpt.c (feraiseexcept): Rename to
__feraiseexcept and define as weak alias of __feraiseexcept. Use
libm_hidden_weak.
* sysdeps/m68k/coldfire/fpu/fraiseexcpt.c (feraiseexcept):
Likewise.
* sysdeps/microblaze/math_private.h (__feraiseexcept): New macro.
* sysdeps/mips/fpu/fraiseexcpt.c (feraiseexcept): Rename to
__feraiseexcept and define as weak alias of __feraiseexcept. Use
libm_hidden_weak.
* sysdeps/powerpc/fpu/fraiseexcpt.c (__feraiseexcept): Use
libm_hidden_def.
* sysdeps/powerpc/nofpu/fraiseexcpt.c (__feraiseexcept): Likewise.
* sysdeps/powerpc/powerpc32/e500/nofpu/fraiseexcpt.c
(__feraiseexcept): Likewise.
* sysdeps/s390/fpu/fraiseexcpt.c (feraiseexcept): Rename to
__feraiseexcept and define as weak alias of __feraiseexcept. Use
libm_hidden_weak.
* sysdeps/sh/sh4/fpu/fraiseexcpt.c (feraiseexcept): Likewise.
* sysdeps/sparc/fpu/fraiseexcpt.c (__feraiseexcept): Use
libm_hidden_def.
* sysdeps/tile/math_private.h (__feraiseexcept): New macro.
* sysdeps/unix/sysv/linux/alpha/fraiseexcpt.S (__feraiseexcept):
Use libm_hidden_def.
* sysdeps/x86_64/fpu/fraiseexcpt.c (__feraiseexcept): Use
libm_hidden_def.
(feraiseexcept): Define as weak not strong alias. Use
libm_hidden_weak.
* sysdeps/x86/fpu/bits/fenv.h (__feraiseexcept_invalid_divbyzero):
New inline function. Factored out of ...
(feraiseexcept): ... here. Use __feraiseexcept_invalid_divbyzero.
* sysdeps/x86/fpu/include/bits/fenv.h: New file.
* math/e_scalb.c (invalid_fn): Call __feraiseexcept instead of
feraiseexcept.
* math/w_acos.c (__acos): Likewise.
* math/w_asin.c (__asin): Likewise.
* math/w_ilogb.c (__ilogb): Likewise.
* math/w_j0.c (y0): Likewise.
* math/w_j1.c (y1): Likewise.
* math/w_jn.c (yn): Likewise.
* math/w_log.c (__log): Likewise.
* math/w_log10.c (__log10): Likewise.
* sysdeps/aarch64/fpu/feupdateenv.c (feupdateenv): Likewise.
* sysdeps/aarch64/fpu/math_private.h
(libc_feupdateenv_test_aarch64): Likewise.
* sysdeps/alpha/fpu/feupdateenv.c (__feupdateenv): Likewise.
* sysdeps/arm/fenv_private.h (libc_feupdateenv_test_vfp): Likewise.
* sysdeps/arm/feupdateenv.c (feupdateenv): Likewise.
* sysdeps/ia64/fpu/feupdateenv.c (feupdateenv): Likewise.
* sysdeps/m68k/fpu/feupdateenv.c (__feupdateenv): Likewise.
* sysdeps/mips/fpu/feupdateenv.c (feupdateenv): Likewise.
* sysdeps/powerpc/fpu/e_sqrt.c (__slow_ieee754_sqrt): Likewise.
* sysdeps/s390/fpu/feupdateenv.c (feupdateenv): Likewise.
* sysdeps/sh/sh4/fpu/feupdateenv.c (feupdateenv): Likewise.
* sysdeps/sparc/fpu/feupdateenv.c (__feupdateenv): Likewise.
This patch fixes the __copysignf optimized macro meant to internal libm
usage when used with constant value. Without the explicit cast to
float, if it is used with const double value (for instance, on
s_casinhf.c) double constants will be used and it may lead to precision
issues in some algorithms.
It fixes the following failures on PPC64/POWER7:
Failure: Test: Real part of: cacos_downward (inf + 0 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
Failure: Test: Real part of: cacos_downward (inf - 0 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
Failure: Test: Real part of: cacos_downward (inf + 0.5 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
Failure: Test: Real part of: cacos_downward (inf - 0.5 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
Failure: Test: Real part of: cacos_towardzero (inf + 0 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
Failure: Test: Real part of: cacos_towardzero (inf - 0 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
Failure: Test: Real part of: cacos_towardzero (inf + 0.5 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
Failure: Test: Real part of: cacos_towardzero (inf - 0.5 i)
Result:
is: 1.19209289550781250000e-07 0x1.00000000000000000000p-23
should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0
This patch optimizes the FPSCR update on exception and rounding change
functions by just updating its value if new value if different from
current one. It also optimizes fedisableexcept and feenableexcept by
removing an unecessary FPSCR read.
This patch fixes the powerpc32 optimized nearbyint/nearbyintf bogus
results for FE_DOWNWARD rounding mode. This is due wrong instructions
sequence used in the rounding calculation (two subtractions instead of
adition and a subtraction).
Fixes BZ#16815.
As recently discussed
<https://sourceware.org/ml/libc-alpha/2014-02/msg00670.html>, it
doesn't seem particularly useful for libm-test-ulps files to contain
huge amounts of data on ulps for individual tests; just the global
maximum observed ulps for each function, together with the
verification of exceptions, errno and special results such as
infinities and NaNs for each test, suffices to verify that a
function's behavior on the given test inputs is within the expected
accuracy. Removing this data reduces source tree churn caused by
updates to these files when libm tests are added, and reduces the
frequency with which testsuite additions actually need libm-test-ulps
changes at all.
Accordingly, this patch removes that data, so that individual tests
get checked against the global bounds for the given function and only
generate an error if those are exceeded. Tested x86_64 (including
verifying that if an ulps value is artificially reduced, the tests do
indeed fail as they should and "make regen-ulps" generates the
expected changes).
* math/libm-test.inc (struct ulp_data): Don't refer to ulps for
individual tests in comment.
(libm-test-ulps.h): Don't refer to test_ulps in #include comment.
(prev_max_error): New variable.
(prev_real_max_error): Likewise.
(prev_imag_max_error): Likewise.
(compare_ulp_data): Don't refer to test names in comment.
(find_test_ulps): Remove function.
(find_function_ulps): Likewise.
(find_complex_function_ulps): Likewise.
(init_max_error): Take function name as argument. Look up ulps
for that function.
(print_ulps): Remove function.
(print_max_error): Use prev_max_error instead of calling
find_function_ulps.
(print_complex_max_error): Use prev_real_max_error and
prev_imag_max_error instead of calling find_complex_function_ulps.
(check_float_internal): Take max_ulp parameter instead of calling
find_test_ulps. Don't call print_ulps.
(check_float): Update call to check_float_internal.
(check_complex): Update calls to check_float_internal.
(START): Pass argument to init_max_error.
* math/gen-libm-test.pl (%results): Don't include "kind"
information.
(parse_ulps): Don't handle ulps of individual tests.
(print_ulps_file): Likewise.
(output_ulps): Likewise.
* math/README.libm-test: Update.
* manual/libm-err-tab.pl (parse_ulps): Don't handle ulps of
individual tests.
* sysdeps/aarch64/libm-test-ulps: Remove individual test ulps.
* sysdeps/alpha/fpu/libm-test-ulps: Likewise.
* sysdeps/arm/libm-test-ulps: Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Likewise.
* sysdeps/ia64/fpu/libm-test-ulps: Likewise.
* sysdeps/m68k/coldfire/fpu/libm-test-ulps: Likewise.
* sysdeps/m68k/m680x0/fpu/libm-test-ulps: Likewise.
* sysdeps/microblaze/libm-test-ulps: Likewise.
* sysdeps/mips/mips32/libm-test-ulps: Likewise.
* sysdeps/mips/mips64/libm-test-ulps: Likewise.
* sysdeps/powerpc/fpu/libm-test-ulps: Likewise.
* sysdeps/powerpc/nofpu/libm-test-ulps: Likewise.
* sysdeps/s390/fpu/libm-test-ulps: Likewise.
* sysdeps/sh/libm-test-ulps: Likewise.
* sysdeps/sparc/fpu/libm-test-ulps: Likewise.
* sysdeps/tile/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* sysdeps/hppa/fpu/libm-test-ulps: Remove individual test ulps.
For PPC64, all the wrappers at sysdeps are superfluous: they are
basically the same implementation from math/w_sqrt.c with the
'#ifdef _IEEE_LIBM'. And the power4 version just force the 'fsqrt'
instruction utilization with an inline assembly, which is already
handled by math_private.h __ieee754_sqrt implementation.
This patch helps some math functions performance by adding the libc_fexxx
variant of inline functions to handle both FPU round and exception set/restore
and by using them on the libc_fexxx_ctx functions. It is based on already coded
fexxx family functions for PPC with fpu.
Here is the summary of performance improvements due this patch (measured on a
POWER7 machine):
Before:
cos(): ITERS:9.5895e+07: TOTAL:5116.03Mcy, MAX:77.6cy, MIN:49.792cy, 18744 calls/Mcy
exp(): ITERS:2.827e+07: TOTAL:5187.15Mcy, MAX:494.018cy, MIN:38.422cy, 5450.01 calls/Mcy
pow(): ITERS:6.1705e+07: TOTAL:5144.26Mcy, MAX:171.95cy, MIN:29.935cy, 11994.9 calls/Mcy
sin(): ITERS:8.6898e+07: TOTAL:5117.06Mcy, MAX:83.841cy, MIN:46.582cy, 16982 calls/Mcy
tan(): ITERS:2.9473e+07: TOTAL:5115.39Mcy, MAX:191.017cy, MIN:172.352cy, 5761.63 calls/Mcy
After:
cos(): ITERS:2.05265e+08: TOTAL:5111.37Mcy, MAX:78.754cy, MIN:24.196cy, 40158.5 calls/Mcy
exp(): ITERS:3.341e+07: TOTAL:5170.84Mcy, MAX:476.317cy, MIN:15.574cy, 6461.23 calls/Mcy
pow(): ITERS:7.6153e+07: TOTAL:5129.1Mcy, MAX:147.5cy, MIN:30.916cy, 14847.2 calls/Mcy
sin(): ITERS:1.58816e+08: TOTAL:5115.11Mcy, MAX:1490.39cy, MIN:22.341cy, 31048.4 calls/Mcy
tan(): ITERS:3.4964e+07: TOTAL:5114.18Mcy, MAX:177.422cy, MIN:146.115cy, 6836.68 calls/Mcy
http://sourceware.org/ml/libc-alpha/2013-07/msg00201.html
These two functions oddly test x+1>0 when a double x is >= 0.0, and
similarly when x is negative. I don't see the point of that since the
test should always be true. I also don't see any need to convert x+1
to integer rather than simply using xr+1. Note that the standard
allows these functions to return any value when the input is outside
the range of long long, but it's not too hard to prevent xr+1
overflowing so that's what I've done.
(With rounding mode FE_UPWARD, x+1 can be a lot more than what you
might naively expect, but perhaps that situation was covered by the
x - xrf < 1.0 test.)
* sysdeps/powerpc/fpu/s_llround.c (__llround): Rewrite.
* sysdeps/powerpc/fpu/s_llroundf.c (__llroundf): Rewrite.
http://sourceware.org/ml/libc-alpha/2013-07/msg00200.html
This works around the fact that vsx is disabled in current
little-endian gcc. Also, float constants take 4 bytes in memory
vs. 16 bytes for vector constants, and we don't need to write one lot
of masks for double (register format) and another for float (mem
format).
* sysdeps/powerpc/fpu/s_float_bitwise.h (__float_and_test28): Don't
use vector int constants.
(__float_and_test24, __float_and8, __float_get_exp): Likewise.
http://sourceware.org/ml/libc-alpha/2013-08/msg00083.html
Further replacement of ieee854 macros and unions. These files also
have some optimisations for comparison against 0.0L, infinity and nan.
Since the ABI specifies that the high double of an IBM long double
pair is the value rounded to double, a high double of 0.0 means the
low double must also be 0.0. The ABI also says that infinity and
nan are encoded in the high double, with the low double unspecified.
This means that tests for 0.0L, +/-Infinity and +/-NaN need only check
the high double.
* sysdeps/ieee754/ldbl-128ibm/e_atan2l.c (__ieee754_atan2l): Rewrite
all uses of ieee854 long double macros and unions. Simplify tests
for long doubles that are fully specified by the high double.
* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c (__ieee754_ilogbl): Likewise.
Remove dead code too.
* sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
(__ieee754_ynl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_log10l.c (__ieee754_log10l): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_logl.c (__ieee754_logl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Likewise.
Remove dead code too.
* sysdeps/ieee754/ldbl-128ibm/k_tanl.c (__kernel_tanl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_expm1l.c (__expm1l): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_frexpl.c (__frexpl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_isinf_nsl.c (__isinf_nsl): Likewise.
Simplify.
* sysdeps/ieee754/ldbl-128ibm/s_isinfl.c (___isinfl): Likewise.
Simplify.
* sysdeps/ieee754/ldbl-128ibm/s_log1pl.c (__log1pl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_modfl.c (__modfl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c (__nextafterl): Likewise.
Comment on variable precision.
* sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c (__nexttoward): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c (__nexttowardf):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_remquol.c (__remquol): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c (__scalblnl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c (__scalbnl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Likewise.
* sysdeps/powerpc/fpu/libm-test-ulps: Adjust tan_towardzero ulps.
