There are 2 new input values that require to be marked as
xfail-rounding:ibm128-libgcc as they're known to fail because of libgcc
issues with different rounding modes.
Otherwise, the other tests just need an increase in ULP.
The corner cases included were generated using exhaustive search
for all float/binary32 values on x86_64 (comparing to MPFR for
correct rounding to nearest).
For the j0/j1/y0 functions, only cases with ulp error <= 9 were
included.
Reviewed-by: Carlos O'Donell <carlos@redhat.com>
With mathinline removal there is no need to keep building and testing
inline math tests.
The gen-libm-tests.py support to generate ULP_I_* is removed and all
libm-test-ulps files are updated to longer have the
i{float,double,ldouble} entries. The support for no-test-inline is
also removed from both gen-auto-libm-tests and the
auto-libm-test-out-* were regenerated.
Checked on x86_64-linux-gnu and i686-linux-gnu.
The threshold value at which powf overflows depends on the rounding mode
and the current check did not take this into account. So when the result
was rounded away from zero it could become infinity without setting
errno to ERANGE.
Example: pow(0x1.7ac7cp+5, 23) is 0x1.fffffep+127 + 0.1633ulp
If the result goes above 0x1.fffffep+127 + 0.5ulp then errno is set,
which is fine in nearest rounding mode, but
powf(0x1.7ac7cp+5, 23) is inf in upward rounding mode
powf(-0x1.7ac7cp+5, 23) is -inf in downward rounding mode
and the previous implementation did not set errno in these cases.
The fix tries to avoid affecting the common code path or calling a
function that may introduce a stack frame, so float arithmetics is used
to check the rounding mode and the threshold is selected accordingly.
[BZ #23961]
* math/auto-libm-test-in: Add new test case.
* math/auto-libm-test-out-pow: Regenerated.
* sysdeps/ieee754/flt-32/e_powf.c (__powf): Fix overflow check.
This patch adds the narrowing add functions from TS 18661-1 to glibc's
libm: fadd, faddl, daddl, f32addf64, f32addf32x, f32xaddf64 for all
configurations; f32addf64x, f32addf128, f64addf64x, f64addf128,
f32xaddf64x, f32xaddf128, f64xaddf128 for configurations with
_Float64x and _Float128; __nldbl_daddl for ldbl-opt. As discussed for
the build infrastructure patch, tgmath.h support is deliberately
deferred, and FP_FAST_* macros are not applicable without optimized
function implementations.
Function implementations are added for all relevant pairs of formats
(including certain cases of a format and itself where more than one
type has that format). The main implementations use round-to-odd, or
a trivial computation in the case where both formats are the same or
where the wider format is IBM long double (in which case we don't
attempt to be correctly rounding). The sysdeps/ieee754/soft-fp
implementations use soft-fp, and are used automatically for
configurations without exceptions and rounding modes by virtue of
existing Implies files. As previously discussed, optimized versions
for particular architectures are possible, but not included.
i386 gets a special version of f32xaddf64 to avoid problems with
double rounding (similar to the existing fdim version), since this
function must round just once without an intermediate rounding to long
double. (No such special version is needed for any other function,
because the nontrivial functions use round-to-odd, which does the
intermediate computation with the rounding mode set to round-to-zero,
and double rounding is OK except in round-to-nearest mode, so is OK
for that intermediate round-to-zero computation.) mul and div will
need slightly different special versions for i386 (using round-to-odd
on long double instead of precision control) because of the
possibility of inexact intermediate results in the subnormal range for
double.
To reduce duplication among the different function implementations,
math-narrow.h gets macros CHECK_NARROW_ADD, NARROW_ADD_ROUND_TO_ODD
and NARROW_ADD_TRIVIAL.
In the trivial cases and for any architecture-specific optimized
implementations, the overhead of the errno setting might be
significant, but I think that's best handled through compiler built-in
functions rather than providing separate no-errno versions in glibc
(and likewise there are no __*_finite entry points for these function
provided, __*_finite effectively being no-errno versions at present in
most cases).
Tested for x86_64 and x86, with both GCC 6 and GCC 7. Tested for
mips64 (all three ABIs, both hard and soft float) and powerpc with GCC
7. Tested with build-many-glibcs.py with both GCC 6 and GCC 7.
* math/Makefile (libm-narrow-fns): Add add.
(libm-test-funcs-narrow): Likewise.
* math/Versions (GLIBC_2.28): Add narrowing add functions.
* math/bits/mathcalls-narrow.h (add): Use __MATHCALL_NARROW .
* math/gen-auto-libm-tests.c (test_functions): Add add.
* math/math-narrow.h (CHECK_NARROW_ADD): New macro.
(NARROW_ADD_ROUND_TO_ODD): Likewise.
(NARROW_ADD_TRIVIAL): Likewise.
* sysdeps/ieee754/float128/float128_private.h (__faddl): New
macro.
(__daddl): Likewise.
* sysdeps/ieee754/ldbl-opt/Makefile (libnldbl-calls): Add fadd and
dadd.
(CFLAGS-nldbl-dadd.c): New variable.
(CFLAGS-nldbl-fadd.c): Likewise.
* sysdeps/ieee754/ldbl-opt/Versions (GLIBC_2.28): Add
__nldbl_daddl.
* sysdeps/ieee754/ldbl-opt/nldbl-compat.h (__nldbl_daddl): New
prototype.
* manual/arith.texi (Misc FP Arithmetic): Document fadd, faddl,
daddl, fMaddfN, fMaddfNx, fMxaddfN and fMxaddfNx.
* math/auto-libm-test-in: Add tests of add.
* math/auto-libm-test-out-narrow-add: New generated file.
* math/libm-test-narrow-add.inc: New file.
* sysdeps/i386/fpu/s_f32xaddf64.c: Likewise.
* sysdeps/ieee754/dbl-64/s_f32xaddf64.c: Likewise.
* sysdeps/ieee754/dbl-64/s_fadd.c: Likewise.
* sysdeps/ieee754/float128/s_f32addf128.c: Likewise.
* sysdeps/ieee754/float128/s_f64addf128.c: Likewise.
* sysdeps/ieee754/float128/s_f64xaddf128.c: Likewise.
* sysdeps/ieee754/ldbl-128/s_daddl.c: Likewise.
* sysdeps/ieee754/ldbl-128/s_f64xaddf128.c: Likewise.
* sysdeps/ieee754/ldbl-128/s_faddl.c: Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_daddl.c: Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_faddl.c: Likewise.
* sysdeps/ieee754/ldbl-96/s_daddl.c: Likewise.
* sysdeps/ieee754/ldbl-96/s_faddl.c: Likewise.
* sysdeps/ieee754/ldbl-opt/nldbl-dadd.c: Likewise.
* sysdeps/ieee754/ldbl-opt/nldbl-fadd.c: Likewise.
* sysdeps/ieee754/soft-fp/s_daddl.c: Likewise.
* sysdeps/ieee754/soft-fp/s_fadd.c: Likewise.
* sysdeps/ieee754/soft-fp/s_faddl.c: Likewise.
* sysdeps/powerpc/fpu/libm-test-ulps: Update.
* sysdeps/mach/hurd/i386/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/aarch64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/alpha/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/arm/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/hppa/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/i386/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/ia64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/m68k/coldfire/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/m68k/m680x0/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/microblaze/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/mips/mips32/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/mips/mips64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/nios2/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/powerpc/powerpc32/nofpu/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm-le.abilist: Likewise.
* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/riscv/rv64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/s390/s390-32/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/s390/s390-64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/sh/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/sparc/sparc32/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/sparc/sparc64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/tile/tilegx32/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/tile/tilegx64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Likewise.
* sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Likewise.
Mark 4 catan and catanh tests as xfail-rounding:ibm128-libgcc.
After this patch all catan and catanh tests pass on ibm128.
Regenerated auto-libm-test-out using gmp 6.1.2, mpfr 3.1.5 and upstream
mpc (9ef8030e50),
Tested on powerpc, powerpc64 and powerpc64le.
* math/auto-libm-test-in: Mark some catan and catanh as
xfail-rounding:ibm128-libgcc.
* math/auto-libm-test-out-catan: Regenerate.
* math/auto-libm-test-out-catanh: Likewise.
Bug 21094 reports 3ulp errors of cosf and tanf for certain arguments
near pi/2 arising from the use of an insufficiently accurate range
reduction. (To be clear, this is a quality-of-implementation issue
relating to the apparent intent of those particular cosf and tanf
implementations; 3ulp is within the general glibc accuracy goals, so
not inherently a bug.)
This patch fixes that error by making a wider range of cases use the
existing more accurate range reduction for arguments close to pi/2.
The wider range of values is still narrow enough for the "z -=
pio2_2;" in the more accurate case to be exact, as the code expects.
Tested for x86_64, x86 and mips64; no ulps updates needed (but at
least on mips64, the larger ulps were seen if the tests were added
without the substantive fix).
[BZ #21094]
* sysdeps/ieee754/flt-32/e_rem_pio2f.c (__ieee754_rem_pio2f): Use
24+24+24-bit pi for wider range of values around pi/2.
* math/auto-libm-test-in: Add more tests of cos and tan.
* math/auto-libm-test-out-cos: Regenerated.
* math/auto-libm-test-out-tan: Likewise.
This patch moves tests of catan and catanh with finite inputs (other
than the divide-by-zero cases producing an exact infinity) to using
the auto-libm-test machinery. Each of auto-libm-test-out-catan and
auto-libm-test-out-catanh takes about three seconds to generate on my
system (so in fact it wasn't necessary after all to defer the move to
auto-libm-test-* until the output files were split up by function).
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of catan and catanh.
* math/auto-libm-test-out-catan: New generated file.
* math/auto-libm-test-out-catanh: Likewise.
* math/libm-test-catan.inc (catan_test_data): Use AUTO_TESTS_c_c.
Move tests with finite inputs, except divide-by-zero cases, to
auto-libm-test-in.
* math/libm-test-catanh.inc (catanh_test_data): Likewise.
* math/Makefile (libm-test-funcs-auto): Add catan and catanh.
(libm-test-funcs-noauto): Remove catan and catanh.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of casin and casinh with finite inputs to using
the auto-libm-test machinery. Each of auto-libm-test-out-casin and
auto-libm-test-out-casinh takes about 38 minutes to generate on my
system because of MPC slowness on special cases that appear in the
tests (with MPC 1.0.3; I don't know to what extent current MPC master
might speed it up).
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of casin and casinh.
* math/auto-libm-test-out-casin: New generated file.
* math/auto-libm-test-out-casinh: Likewise.
* math/libm-test-casin.inc (casin_test_data): Use AUTO_TESTS_c_c.
Move tests with finite inputs to auto-libm-test-in.
* math/libm-test-casinh.inc (casinh_test_data): Likewise.
* math/Makefile (libm-test-funcs-auto): Add casin and casinh.
(libm-test-funcs-noauto): Remove casin and casinh.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of cacos and cacosh with finite inputs to using
the auto-libm-test machinery. Each of auto-libm-test-out-cacos and
auto-libm-test-out-cacosh takes about 80 minutes to generate on my
system because of MPC slowness on special cases that appear in the
tests (with MPC 1.0.3; I don't know to what extent current MPC master
might speed it up).
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of cacos and cacosh.
* math/auto-libm-test-out-cacos: New generated file.
* math/auto-libm-test-out-cacosh: Likewise.
* math/libm-test-cacos.inc (cacos_test_data): Use AUTO_TESTS_c_c.
Move tests with finite inputs to auto-libm-test-in.
* math/libm-test-cacosh.inc (cacosh_test_data): Likewise.
* math/Makefile (libm-test-funcs-auto): Add cacos and cacosh.
(libm-test-funcs-noauto): Remove cacos and cacosh.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
When I moved tests of csin and csinh to auto-libm-test-in, I didn't
move a few tests for which gen-auto-libm-tests was very slow because
of MPC slowness on certain inputs.
Now that auto-libm-test-out has been split up, such slowness only
affects regenerating the test expectations for the individual
functions in question, rather than any addition of tests for any
function to auto-libm-test-in. Thus, I no longer consider it a
problem to have these inputs in auto-libm-test-in, and this patch
moves them there. This results in test generation for csin and csinh
taking 5m43s (for each of csin and csinh) on my system, while other
functions are unaffected.
I expect the test generation to be much faster in MPC 1.1 (the
relevant performance improvements went in MPC mainline in Dec 2013,
but there hasn't been a release from mainline since then).
Tested for x86_64 and x86.
* math/auto-libm-test-in: Add more tests of csin and csinh.
* math/auto-libm-test-out-csin: Regenerated.
* math/auto-libm-test-out-csinh: Likewise.
* math/libm-test-csin.inc (csin_test_data): Remove tests moved to
auto-libm-test-in.
* math/libm-test-csinh.inc (csinh_test_data): Likewise.
Bug 21112 reports a case where powf is substantially inaccurate. This
results from a multiplication where cp_h*p_h is required to be exact,
and p_h is masked to have only 12 leading nonzero bits in its
mantissa, but the value of cp_h has the 13th bit nonzero, leading to
inexact multiplication results in some cases that can result in large
errors in the final result of powf. This patch fixes this by using a
value of cp_h correctly rounded to nearest to 12 bits, with a
corresponding updated value of cp_l.
Tested for x86_64 and x86.
[BZ #21112]
* sysdeps/ieee754/flt-32/e_powf.c (cp_h): Use value with trailing
12 bits zero.
(cp_l): Update for new value of cp_h.
* math/auto-libm-test-in: Add another test of pow.
* math/auto-libm-test-out-pow: Regenerated.
This patch further improves XFAILing for ibm128-libgcc of tests in
auto-libm-test-*.
The bulk of the cases needing XFAILing are
xfail-rounding:ibm128-libgcc used for inputs where (possibly after
rounding the inputs to another floating-point type) the result
overflows (and the result in non-default rounding modes may be wildly
wrong with unpatched libgcc) or underflows near 0 (and the result in
non-default rounding modes may end up having the wrong sign). This
patch makes gen-auto-libm-tests detect such cases and apply
xfail-rounding:ibm128-libgcc automatically to them, so most of the
manual XFAILs in auto-libm-test-in are no longer needed (some are
still needed if e.g. the result is very close to overflow, resulting
in an internal overflow in libgcc in some rounding modes). A few
manual XFAILs are added for cases not covered by this
gen-auto-libm-tests change, and a few existing such XFAILs are left
in.
Tested for powerpc.
* math/gen-auto-libm-tests.c (output_for_one_input_case): Apply
xfail-rounding:ibm128-libgcc automatically to tests overflowing
and those that can underflow to zero.
* math/auto-libm-test-in: Remove most XFAILs for ibm128-libgcc and
add others.
* math/auto-libm-test-out: Regenerated.
This patch cleans up and updates the libm-test XFAILs for the ibm128
format. More of them are changed to use a new ibm128-libgcc
conditional, to reflect that they are not in fact needed if you've
patched libgcc to fix the known issues (at substantial performance
cost). Many additional XFAILs are added for tests that fail with
unpatched libgcc (most but not all of them xfail-rounding).
Note that further such fixes will be needed for test-ldouble actually
to pass with default libgcc (in particular, XFAILs for pow tests and
for various affected tests directly embedded in libm-test.inc). With
patched libgcc, there may be a few XFAILs needed but the results are
already substantially clean apart from a few ulps differences.
Tested for powerpc.
* math/libm-test.inc (TEST_COND_ibm128_libgcc): New macro.
(init_max_error) [TEST_COND_ibm128]: Increase maximum error
allowed to 16 ulps.
* math/auto-libm-test-in: Change most XFAILs for ibm128 to use
ibm128-libgcc. XFAIL more tests for ibm128-libgcc.
* math/auto-libm-test-out: Regenerated.
During the sincos consolidation I made two mistakes, one was a logical
error due to which cos(0x1.8475e5afd4481p+0) returned
sin(0x1.8475e5afd4481p+0) instead.
The second issue was an error in negating inputs for the correct
quadrants for sine. I could not find a suitable test case for this
despite running a program to search for such an input for a couple of
hours.
Following patch fixes both issues. Tested on x86_64. Thanks to Matt
Clay for identifying the issue.
[BZ #20357]
* sysdeps/ieee754/dbl-64/s_sin.c (sloww): Fix up condition
to call __mpsin/__mpcos and to negate values.
* math/auto-libm-test-in: Add test.
* math/auto-libm-test-out: Regenerate.
Apply the following sed regexes to auto-libm-test-in in order:
s/flt-32/binary32/
s/dbl-64/binary64/
s/ldbl-96-intel/intel96/
s/ldbl-96-m68k/m68k96/
s/ldbl-128ibm/ibm128/
s/ldbl-128/binary128/
and fixup ldbl-96 comment manually.
ldbl-128ibm had an implementation of fmal that just did (x * y) + z in
most cases, with no attempt at actually being a fused operation.
This patch replaces it with a genuine fused operation. It is not
necessarily correctly rounding, but should produce a result at least
as accurate as the long double arithmetic operations in libgcc, which
I think is all that can reasonably be expected for such a non-IEEE
format where arithmetic is approximate rather than rounded according
to any particular rule for determining the exact result. Like the
libgcc arithmetic, it may produce spurious overflow and underflow
results, and it falls back to the libgcc multiplication in the case of
(finite, finite, zero).
This concludes the fixes for bug 13304; any subsequently found fma
issues should go in separate Bugzilla bugs. Various other pieces of
bug 13304 were fixed in past releases over the past several years.
Tested for powerpc.
[BZ #13304]
* sysdeps/ieee754/ldbl-128ibm/s_fmal.c: Include <fenv.h>,
<float.h>, <math_private.h> and <stdlib.h>.
(add_split): New function.
(mul_split): Likewise.
(ext_val): New typedef.
(store_ext_val): New function.
(mul_ext_val): New function.
(compare): New function.
(add_split_ext): New function.
(__fmal): After checking for Inf, NaN and zero, compute result as
an exact sum of scaled double values in round-to-nearest before
adding those up and adjusting for other rounding modes.
* math/auto-libm-test-in: Remove xfail-rounding:ldbl-128ibm from
tests of fma.
* math/auto-libm-test-out: Regenerated.
Bug 19848 reports cases where powl on x86 / x86_64 has error
accumulation, for small integer exponents, larger than permitted by
glibc's accuracy goals, at least in some rounding modes. This patch
further restricts the exponent range for which the
small-integer-exponent logic is used to limit the possible error
accumulation.
Tested for x86_64 and x86 and ulps updated accordingly.
[BZ #19848]
* sysdeps/i386/fpu/e_powl.S (p3): Rename to p2 and change value
from 8 to 4.
(__ieee754_powl): Compare integer exponent against 4 not 8.
* sysdeps/x86_64/fpu/e_powl.S (p3): Rename to p2 and change value
from 8 to 4.
(__ieee754_powl): Compare integer exponent against 4 not 8.
* math/auto-libm-test-in: Add more tests of pow.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
Prompted by a gcc-patches discussion, this patch adds tests of pow for
the cases where pow (x, 0.5) is required to return a different result
from sqrt (x), as those cases were previously missing from the tests
(although they worked correctly).
Tested for x86_64 and x86.
* math/auto-libm-test-in: Add another test of pow.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (pow_test_data): Add another test.
j1 and jn can underflow for small arguments, but fail to set errno
when underflowing to 0. This patch fixes them to set errno in that
case.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #18611]
* sysdeps/ieee754/dbl-64/e_j1.c (__ieee754_j1): Set errno and
avoid excess range and precision on underflow.
* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Likewise.
* sysdeps/ieee754/flt-32/e_j1f.c (__ieee754_j1f): Likewise.
* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): Set errno on
underflow.
* sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
* sysdeps/ieee754/ldbl-96/e_j1l.c (__ieee754_j1l): Likewise.
* sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise.
* math/auto-libm-test-in: Do not allow missing errno setting for
tests of j1 and jn.
* math/auto-libm-test-out: Regenerated.
This patch improves the libm test coverage for a few more functions.
Tested for x86_64 and x86.
2015-10-21 Joseph Myers <joseph@codesourcery.com>
* math/auto-libm-test-in: Add more tests of hypot, j0, j1, jn,
log, log10 and log2.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (fmod_test_data): Add more tests.
(fpclassify_test_data): Likewise.
(frexp_test_data): Likewise.
(hypot_test_data): Likewise.
(ilogb_test_data): Likewise.
The ldbl-128 / ldbl-128ibm implementation of lgamma has problems with
its handling of large arguments. It has an overflow threshold that is
correct only for ldbl-128, despite being used for both types - with
diagnostic control macros as a temporary measure to disable warnings
about that constant overflowing for ldbl-128ibm - and it has a
calculation that's roughly x * log(x) - x, resulting in overflows for
arguments that are roughly at most a factor 1/log(threshold) below the
overflow threshold.
This patch fixes both issues, using an overflow threshold appropriate
for the type in question and adding another case for large arguments
that avoids the possible intermediate overflow.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #16347]
[BZ #19046]
* sysdeps/ieee754/ldbl-128/e_lgammal_r.c: Do not include
<libc-internal.h>.
(MAXLGM): Do not use diagnostic control macros.
[LDBL_MANT_DIG == 106] (MAXLGM): Change value to overflow
threshold for ldbl-128ibm.
(__ieee754_lgammal_r): For large arguments, multiply by log - 1
instead of multiplying by log then subtracting.
* math/auto-libm-test-in: Add more tests of lgamma.
* math/auto-libm-test-out: Regenerated.
This patch improves test coverage of the real libm functions [a-e]*,
ensuring that special cases and ranges of input values of potential
significance (such as close to overflow and underflow thresholds) are
more systematically covered.
This is a followup to
<https://sourceware.org/ml/libc-alpha/2013-12/msg00757.html> which
covered [a-c]* (however, I found more weaknesses in the coverage of
those functions when preparing this patch, hence the additional tests
being added for them here).
Addition of a test for acosh (-qNaN) is temporarily deferred, to be
included as part of a fix for bug 19032 which was discovered in the
course of adding these tests (and which illustrates the use of testing
-qNaN as well as +qNaN as input even to functions for which the sign
of a NaN isn't meant to be significant).
Tested for x86_64 and x86.
* math/auto-libm-test-in: Add more tests of acos, acosh, asin,
atan, atan2, atanh, cbrt, cos, cosh, erf, erfc, exp, exp10, exp2
and expm1.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (acos_test_data): Add more tests.
(asin_test_data): Likewise.
(asinh_test_data): Likewise.
(atan_test_data): Likewise.
(atanh_test_data): Likewise.
(atan2_test_data): Likewise.
(cbrt_test_data): Likewise.
(ceil_test_data): Likewise.
(copysign_test_data): Likewise.
(cos_test_data): Likewise.
(cosh_test_data): Likewise.
(erf_test_data): Likewise.
(erfc_test_data): Likewise.
(exp_test_data): Likewise.
(exp10_test_data): Likewise.
(exp2_test_data): Likewise.
(expm1_test_data): Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
For arguments with X^2 + Y^2 close to 1, clog and clog10 avoid large
errors from log(hypot) by computing X^2 + Y^2 - 1 in a way that avoids
cancellation error and then using log1p.
However, the thresholds for using that approach still result in log
being used on argument as large as sqrt(13/16) > 0.9, leading to
significant errors, in some cases above the 9ulp maximum allowed in
glibc libm. This patch arranges for the approach using log1p to be
used in any cases where |X|, |Y| < 1 and X^2 + Y^2 >= 0.5 (with the
existing allowance for cases where one of X and Y is very small),
adjusting the __x2y2m1 functions to work with the wider range of
inputs. This way, log only gets used on arguments below sqrt(1/2) (or
substantially above 1), where the error involved is much less.
Tested for x86_64, x86, mips64 and powerpc. For the ulps regeneration
I removed the existing clog and clog10 ulps before regenerating to
allow any reduced ulps to appear. Tests added include those found by
random test generation to produce large ulps either before or after
the patch, and some found by trying inputs close to the (0.75, 0.5)
threshold where the potential errors from using log are largest.
[BZ #19016]
* sysdeps/generic/math_private.h (__x2y2m1f): Update comment to
allow more cases with X^2 + Y^2 >= 0.5.
* sysdeps/ieee754/dbl-64/x2y2m1.c (__x2y2m1): Likewise. Add -1 as
normal element in sum instead of special-casing based on values of
arguments.
* sysdeps/ieee754/dbl-64/x2y2m1f.c (__x2y2m1f): Update comment.
* sysdeps/ieee754/ldbl-128/x2y2m1l.c (__x2y2m1l): Likewise. Add
-1 as normal element in sum instead of special-casing based on
values of arguments.
* sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c (__x2y2m1l): Likewise.
* sysdeps/ieee754/ldbl-96/x2y2m1.c [FLT_EVAL_METHOD != 0]
(__x2y2m1): Update comment.
* sysdeps/ieee754/ldbl-96/x2y2m1l.c (__x2y2m1l): Likewise. Add -1
as normal element in sum instead of special-casing based on values
of arguments.
* math/s_clog.c (__clog): Handle more cases using log1p without
hypot.
* math/s_clog10.c (__clog10): Likewise.
* math/s_clog10f.c (__clog10f): Likewise.
* math/s_clog10l.c (__clog10l): Likewise.
* math/s_clogf.c (__clogf): Likewise.
* math/s_clogl.c (__clogl): Likewise.
* math/auto-libm-test-in: Add more tests of clog and clog10.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The flt-32 version of powf can be inaccurate because of bugs in the
extra-precision calculation of (x-1)/(x+1) or (x-1.5)/(x+1.5) as part
of calculating log(x) with extra precision: a constant used (as part
of adding 1 or 1.5 through integer arithmetic) is incorrect, and then
the code fails to mask a computed high part before using it in
arithmetic that relies on s_h*t_h being exactly representable. This
patch fixes these bugs.
Tested for x86_64 and x86. x86_64 ulps for powf removed and
regenerated to reflect reduced ulps from the increased accuracy for
existing tests.
[BZ #18956]
* sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): Add 0x00400000
not 0x0040000 for high bit of mantissa. Mask with 0xfffff000 when
extracting high part.
* math/auto-libm-test-in: Add another test of pow.
* math/auto-libm-test-out: Regenerated.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
Similar to various other bugs in this area, pow functions can fail to
raise the underflow exception when the result is tiny and inexact but
one or more low bits of the intermediate result that is scaled down
(or, in the i386 case, converted from a wider evaluation format) are
zero. This patch forces the exception in a similar way to previous
fixes, thereby concluding the fixes for known bugs with missing
underflow exceptions currently filed in Bugzilla.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #18825]
* sysdeps/i386/fpu/i386-math-asm.h (FLT_NARROW_EVAL_UFLOW_NONNAN):
New macro.
(DBL_NARROW_EVAL_UFLOW_NONNAN): Likewise.
(LDBL_CHECK_FORCE_UFLOW_NONNAN): Likewise.
* sysdeps/i386/fpu/e_pow.S: Use DEFINE_DBL_MIN.
(__ieee754_pow): Use DBL_NARROW_EVAL_UFLOW_NONNAN instead of
DBL_NARROW_EVAL, reloading the PIC register as needed.
* sysdeps/i386/fpu/e_powf.S: Use DEFINE_FLT_MIN.
(__ieee754_powf): Use FLT_NARROW_EVAL_UFLOW_NONNAN instead of
FLT_NARROW_EVAL. Use separate return path for case when first
argument is NaN.
* sysdeps/i386/fpu/e_powl.S: Include <i386-math-asm.h>. Use
DEFINE_LDBL_MIN.
(__ieee754_powl): Use LDBL_CHECK_FORCE_UFLOW_NONNAN, reloading the
PIC register.
* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Use
math_check_force_underflow_nonneg.
* sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): Force
underflow for subnormal result.
* sysdeps/ieee754/ldbl-128/e_powl.c (__ieee754_powl): Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Use
math_check_force_underflow_nonneg.
* sysdeps/x86/fpu/powl_helper.c (__powl_helper): Use
math_check_force_underflow.
* sysdeps/x86_64/fpu/x86_64-math-asm.h
(LDBL_CHECK_FORCE_UFLOW_NONNAN): New macro.
* sysdeps/x86_64/fpu/e_powl.S: Include <x86_64-math-asm.h>. Use
DEFINE_LDBL_MIN.
(__ieee754_powl): Use LDBL_CHECK_FORCE_UFLOW_NONNAN.
* math/auto-libm-test-in: Add more tests of pow.
* math/auto-libm-test-out: Regenerated.
Similar to various other bugs in this area, hypot functions can fail
to raise the underflow exception when the result is tiny and inexact
but one or more low bits of the intermediate result that is scaled
down (or, in the i386 case, converted from a wider evaluation format)
are zero. This patch forces the exception in a similar way to
previous fixes.
Note that this issue cannot arise for implementations of hypotf using
double (or wider) for intermediate evaluation (if hypotf should
underflow, that means the double square root is being computed of some
number of the form N*2^-298, for 0 < N < 2^46, which is exactly
represented as a double, and whatever the rounding mode such a square
root cannot have a mantissa with all zeroes after the initial 23
bits). Thus no changes are made to hypotf implementations in this
patch, only to hypot and hypotl.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #18803]
* sysdeps/i386/fpu/e_hypot.S: Use DEFINE_DBL_MIN.
(MO): New macro.
(__ieee754_hypot) [PIC]: Load PIC register.
(__ieee754_hypot): Use DBL_NARROW_EVAL_UFLOW_NONNEG instead of
DBL_NARROW_EVAL.
* sysdeps/ieee754/dbl-64/e_hypot.c (__ieee754_hypot): Use
math_check_force_underflow_nonneg in case where result might be
tiny.
* sysdeps/ieee754/ldbl-128/e_hypotl.c (__ieee754_hypotl):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c (__ieee754_hypotl):
Likewise.
* sysdeps/ieee754/ldbl-96/e_hypotl.c (__ieee754_hypotl): Likewise.
* sysdeps/powerpc/fpu/e_hypot.c (__ieee754_hypot): Likewise.
* math/auto-libm-test-in: Add more tests of hypot.
* math/auto-libm-test-out: Regenerated.
Similar to various other bugs in this area, tgamma functions can fail
to raise the underflow exception when the result is tiny and inexact
but one or more low bits of the intermediate result that is scaled
down are zero. This patch forces the exception in a similar way to
previous fixes.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #18951]
* sysdeps/ieee754/dbl-64/e_gamma_r.c (__ieee754_gamma_r): Force
underflow exception for small results.
* sysdeps/ieee754/flt-32/e_gammaf_r.c (__ieee754_gammaf_r):
Likewise.
* sysdeps/ieee754/ldbl-128/e_gammal_r.c (__ieee754_gammal_r):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r):
Likewise.
* sysdeps/ieee754/ldbl-96/e_gammal_r.c (__ieee754_gammal_r):
Likewise.
* math/auto-libm-test-in: Add more tests of tgamma.
* math/auto-libm-test-out: Regenerated.
Similar to various other bugs in this area, ctan and ctanh can fail to
raise the underflow exception for some cases of results that are tiny
and inexact. This patch forces the exception in a similar way to
previous fixes.
Tested for x86_64 and x86.
[BZ #18595]
* math/s_ctan.c (__ctan): Force underflow exception for results
whose real or imaginary part has small absolute value.
* math/s_ctanf.c (__ctanf): Likewise.
* math/s_ctanh.c (__ctanh): Likewise.
* math/s_ctanhf.c (__ctanhf): Likewise.
* math/s_ctanhl.c (__ctanhl): Likewise.
* math/s_ctanl.c (__ctanl): Likewise.
* math/auto-libm-test-in: Do not allow missing underflow for ctan
and ctanh. Add more tests of ctan and ctanh.
On i386, the double version of exp10 can miss underflow exceptions if
the result is in the subnormal range for double but the last 11 bits
of the 64-bit extended-precision mantissa happen to be zero. This
patch forces the exception in a similar way to previous fixes.
As with the exp2 and exp fixes, the exp10f changes may in fact not be
needed to ensure underflow exceptions, but are included for
consistency and to fix the exp10 part of bug 18875 by ensuring that
excess range and precision is removed from underflowing return values.
Tested for x86_64 and x86.
[BZ #18875]
[BZ #18966]
* sysdeps/i386/fpu/e_exp10.S (dbl_min): New object.
(MO): New macro.
(__ieee754_exp10): For small results, force underflow exception
and remove excess range and precision from return value.
* sysdeps/i386/fpu/e_exp10f.S (flt_min): New object.
(MO): New macro.
(__ieee754_exp10f): For small results, force underflow exception
and remove excess range and precision from return value.
* math/auto-libm-test-in: Add more tests of exp10.
* math/auto-libm-test-out: Regenerated.
On i386, the double version of exp can miss underflow exceptions if
the result is in the subnormal range for double but the last 11 bits
of the 64-bit extended-precision mantissa happen to be zero. This
patch forces the exception in a similar way to previous fixes.
As with the exp2 fixes, the expf changes may in fact not be needed to
ensure underflow exceptions, but are included for consistency and to
fix the exp part of bug 18875 by ensuring that excess range and
precision is removed from underflowing return values.
Tested for x86_64 and x86.
[BZ #18875]
[BZ #18961]
* sysdeps/i386/fpu/e_exp.S (dbl_min): New object.
(MO): New macro.
(__ieee754_exp): For small results, force underflow exception and
remove excess range and precision from return value.
(__exp_finite): Likewise.
* sysdeps/i386/fpu/e_expf.S (flt_min): New object.
(MO): New macro.
(__ieee754_expf): For small results, force underflow exception and
remove excess range and precision from return value.
(__expf_finite): Likewise.
* math/auto-libm-test-in: Add more tests of exp.
* math/auto-libm-test-out: Regenerated.
Various exp2 implementations in glibc can miss underflow exceptions
when the scaling down part of the calculation is exact (or, in the x86
case, when the conversion from extended precision to the target
precision is exact). This patch forces the exception in a similar way
to previous fixes.
The x86 exp2f changes may in fact not be needed for this purpose -
it's likely to be the case that no argument of type float has an exp2
result so close to an exact subnormal float value that it equals that
value when rounded to 64 bits (even taking account of variation
between different x86 implementations). However, they are included
for consistency with the changes to exp2 and so as to fix the exp2f
part of bug 18875 by ensuring that excess range and precision is
removed from underflowing return values.
Tested for x86_64, x86 and mips64.
[BZ #16521]
[BZ #18875]
* math/e_exp2l.c (__ieee754_exp2l): Force underflow exception for
small results.
* sysdeps/i386/fpu/e_exp2.S (dbl_min): New object.
(MO): New macro.
(__ieee754_exp2): For small results, force underflow exception and
remove excess range and precision from return value.
* sysdeps/i386/fpu/e_exp2f.S (flt_min): New object.
(MO): New macro.
(__ieee754_exp2f): For small results, force underflow exception
and remove excess range and precision from return value.
* sysdeps/i386/fpu/e_exp2l.S (ldbl_min): New object.
(MO): New macro.
(__ieee754_exp2l): Force underflow exception for small results.
* sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Likewise.
* sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise.
* sysdeps/x86_64/fpu/e_exp2l.S (ldbl_min): New object.
(MO): New macro.
(__ieee754_exp2l): Force underflow exception for small results.
* math/auto-libm-test-in: Add more tests or exp2.
* math/auto-libm-test-out: Regenerated.
This patch adds more libm test inputs found through random test
generation to increase previously known ulps. This particular test
generation was run for mips64, so most of the increased ulps are for
ldbl-128 (float and double having been fairly well covered by such
testing for x86_64), but there's the odd ulps increase for other
formats.
Tested for x86_64, x86 and mips64.
* math/auto-libm-test-in: Add more tests of acos, acosh, asin,
asinh, atan, atan2, atanh, cabs, carg, cos, csqrt, erfc, exp,
exp10, exp2, log, log1p, log2, pow, sin, sincos, sinh, tan and
tanh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/mips/mips32/libm-test-ulps: Likewise.
* sysdeps/mips/mips64/libm-test-ulps: Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The ldbl-128 / ldbl-128ibm implementation of lgammal converts (the
floor of minus) non-integer negative arguments to int to determine the
value of signgam. When those values are outside the range of int,
this produces spurious "invalid" exceptions and incorrect values of
signgam. This patch fixes this by instead determining signgam through
comparing half the integer in question to floor of half the integer.
Tested for mips64, x86_64 and x86.
[BZ #18952]
* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r): Do
not convert non-integer negative arguments to int to determine the
value of signgam.
* math/auto-libm-test-in: Add more tests of lgamma.
* math/auto-libm-test-out: Regenerated.
This patch adds more libm test inputs found through random test
generation to increase observed ulps on x86_64.
Tested for x86_64 and x86.
* math/auto-libm-test-in: Add more tests of acosh, atanh, cbrt,
cosh, csqrt, erfc, expm1 and lgamma.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The existing implementations of lgamma functions (except for the ia64
versions) use the reflection formula for negative arguments. This
suffers large inaccuracy from cancellation near zeros of lgamma (near
where the gamma function is +/- 1).
This patch fixes this inaccuracy. For arguments above -2, there are
no zeros and no large cancellation, while for sufficiently large
negative arguments the zeros are so close to integers that even for
integers +/- 1ulp the log(gamma(1-x)) term dominates and cancellation
is not significant. Thus, it is only necessary to take special care
about cancellation for arguments around a limited number of zeros.
Accordingly, this patch uses precomputed tables of relevant zeros,
expressed as the sum of two floating-point values. The log of the
ratio of two sines can be computed accurately using log1p in cases
where log would lose accuracy. The log of the ratio of two gamma(1-x)
values can be computed using Stirling's approximation (the difference
between two values of that approximation to lgamma being computable
without computing the two values and then subtracting), with
appropriate adjustments (which don't reduce accuracy too much) in
cases where 1-x is too small to use Stirling's approximation directly.
In the interval from -3 to -2, using the ratios of sines and of
gamma(1-x) can still produce too much cancellation between those two
parts of the computation (and that interval is also the worst interval
for computing the ratio between gamma(1-x) values, which computation
becomes more accurate, while being less critical for the final result,
for larger 1-x). Because this can result in errors slightly above
those accepted in glibc, this interval is instead dealt with by
polynomial approximations. Separate polynomial approximations to
(|gamma(x)|-1)(x-n)/(x-x0) are used for each interval of length 1/8
from -3 to -2, where n (-3 or -2) is the nearest integer to the
1/8-interval and x0 is the zero of lgamma in the relevant half-integer
interval (-3 to -2.5 or -2.5 to -2).
Together, the two approaches are intended to give sufficient accuracy
for all negative arguments in the problem range. Outside that range,
the previous implementation continues to be used.
Tested for x86_64, x86, mips64 and powerpc. The mips64 and powerpc
testing shows up pre-existing problems for ldbl-128 and ldbl-128ibm
with large negative arguments giving spurious "invalid" exceptions
(exposed by newly added tests for cases this patch doesn't affect the
logic for); I'll address those problems separately.
[BZ #2542]
[BZ #2543]
[BZ #2558]
* sysdeps/ieee754/dbl-64/e_lgamma_r.c (__ieee754_lgamma_r): Call
__lgamma_neg for arguments from -28.0 to -2.0.
* sysdeps/ieee754/flt-32/e_lgammaf_r.c (__ieee754_lgammaf_r): Call
__lgamma_negf for arguments from -15.0 to -2.0.
* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
Call __lgamma_negl for arguments from -48.0 or -50.0 to -2.0.
* sysdeps/ieee754/ldbl-96/e_lgammal_r.c (__ieee754_lgammal_r):
Call __lgamma_negl for arguments from -33.0 to -2.0.
* sysdeps/ieee754/dbl-64/lgamma_neg.c: New file.
* sysdeps/ieee754/dbl-64/lgamma_product.c: Likewise.
* sysdeps/ieee754/flt-32/lgamma_negf.c: Likewise.
* sysdeps/ieee754/flt-32/lgamma_productf.c: Likewise.
* sysdeps/ieee754/ldbl-128/lgamma_negl.c: Likewise.
* sysdeps/ieee754/ldbl-128/lgamma_productl.c: Likewise.
* sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c: Likewise.
* sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c: Likewise.
* sysdeps/ieee754/ldbl-96/lgamma_negl.c: Likewise.
* sysdeps/ieee754/ldbl-96/lgamma_product.c: Likewise.
* sysdeps/ieee754/ldbl-96/lgamma_productl.c: Likewise.
* sysdeps/generic/math_private.h (__lgamma_negf): New prototype.
(__lgamma_neg): Likewise.
(__lgamma_negl): Likewise.
(__lgamma_product): Likewise.
(__lgamma_productl): Likewise.
* math/Makefile (libm-calls): Add lgamma_neg and lgamma_product.
* math/auto-libm-test-in: Add more tests of lgamma.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The csqrt implementations in glibc can miss underflow exceptions when
the real or imaginary part of the result becomes tiny in the course of
scaling down (in particular, multiplication by 0.5) and that scaling
is exact although the relevant part of the mathematical result isn't.
This patch forces the exception in a similar way to previous fixes.
Tested for x86_64 and x86.
[BZ #18370]
* math/s_csqrt.c (__csqrt): Force underflow exception for results
whose real or imaginary part has small absolute value.
* math/s_csqrtf.c (__csqrtf): Likewise.
* math/s_csqrtl.c (__csqrtl): Likewise.
* math/auto-libm-test-in: Add more tests of csqrt.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
The csqrt functions scale up small arguments to avoid underflows when
calling hypot functions. However, even when hypot does not underflow,
a subsequent calculation of 0.5 * hypot can underflow. This patch
duly increases the threshold and scale factor to avoid such underflows
as well.
Tested for x86_64, x86 and mips64.
[BZ #18823]
* math/s_csqrt.c (__csqrt): Increase threshold and scale factor
for scaling up small arguments.
* math/s_csqrtf.c (__csqrtf): Likewise.
* math/s_csqrtl.c (__csqrtl): Likewise.
* math/auto-libm-test-in: Add more tests of csqrt.
* math/auto-libm-test-out: Regenerated.
Various fma implementations have logic that, when computing fma (x, y,
z) where z is large (so care needs taking to avoid internal overflow)
but x * y is small, scale x * y up instead of down to avoid internal
underflows resulting from scaling down. (In these cases, x * y is
small enough that only its sign actually matters rather than the exact
value.)
The threshold for scaling up instead of down was correct for "if the
unscaled values were multiplied, the low part of the multiplication
could underflow", and the scaling was sufficient to ensure that the
low part of the multiplication did not underflow (given that cases of
very small x * y - less than half the least subnormal - were
previously dealt with). However, the choice in the functions wasn't
between scaling up or no scaling, but between scaling up and scaling
down (scaling down actually being needed when x * y isn't so small
compared to z and so the exact value does matter). Thus a larger
threshold is needed to ensure that scaling down doesn't produce values
the multiplication of whose low parts underflows. This patch
increases the thresholds accordingly.
Tested for x86_64, x86 and mips64 (with the MIPS version of s_fmal.c
removed so that the ldbl-128 version gets tested instead of the
soft-fp one).
[BZ #18824]
* sysdeps/ieee754/dbl-64/s_fma.c (__fma): Increase threshold for
scaling x * y up instead of down.
* sysdeps/ieee754/ldbl-128/s_fmal.c (__fmal): Likewise.
* sysdeps/ieee754/ldbl-96/s_fmal.c (__fmal): Likewise.
* math/auto-libm-test-in: Add more tests of fma.
* math/auto-libm-test-out: Regenerated.
