In the ldbl-128 implementation of expm1l, when expm1l's result should
underflow to 0 (argument minus the least subnormal, in some rounding
modes), it can be a zero of the wrong sign. This patch fixes this in
the same way previously used for the x86 / x86_64 versions.
Tested for mips64.
[BZ #18619]
* sysdeps/ieee754/ldbl-128/s_expm1l.c (__expm1l): Force underflow
and return argument in case of subnormal argument.
In non-default rounding modes, tgamma can be slightly less accurate
than permitted by glibc's accuracy goals.
Part of the problem is error accumulation, addressed in this patch by
setting round-to-nearest for internal computations. However, there
was also a bug in the code dealing with computing pow (x + n, x + n)
where x + n is not exactly representable, providing another source of
error even in round-to-nearest mode; it was necessary to address both
bugs to get errors for all testcases within glibc's accuracy goals.
Given this second fix, accuracy in round-to-nearest mode is also
improved (hence regeneration of ulps for tgamma should be from scratch
- truncate libm-test-ulps or at least remove existing tgamma entries -
so that the expected ulps can be reduced).
Some additional complications also arose. Certain tgamma tests should
strictly, according to IEEE semantics, overflow or not depending on
the rounding mode; this is beyond the scope of glibc's accuracy goals
for any function without exactly-determined results, but
gen-auto-libm-tests doesn't handle being lax there as it does for
underflow. (libm-test.inc also doesn't handle being lax about whether
the result in cases very close to the overflow threshold is infinity
or a finite value close to overflow, but that doesn't cause problems
in this case though I've seen it cause problems with random test
generation for some functions.) Thus, spurious-overflow markings,
with a comment, are added to auto-libm-test-in (no bug in Bugzilla
because the issue is with the testsuite, not a user-visible bug in
glibc). And on x86, after the patch I saw ERANGE issues as previously
reported by Carlos (see my commentary in
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>), which
needed addressing by ensuring excess range and precision were
eliminated at various points if FLT_EVAL_METHOD != 0.
I also noticed and fixed a cosmetic issue where 1.0f was used in long
double functions and should have been 1.0L.
This completes the move of all functions to testing in all rounding
modes with ALL_RM_TEST, so gen-libm-have-vector-test.sh is updated to
remove the workaround for some functions not using ALL_RM_TEST.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #18613]
* sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Take log of
X_ADJ not X when adjusting exponent.
(__ieee754_gamma_r): Do intermediate computations in
round-to-nearest then adjust overflowing and underflowing results
as needed.
* sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Take log
of X_ADJ not X when adjusting exponent.
(__ieee754_gammaf_r): Do intermediate computations in
round-to-nearest then adjust overflowing and underflowing results
as needed.
* sysdeps/ieee754/ldbl-128/e_gammal_r.c (gammal_positive): Take
log of X_ADJ not X when adjusting exponent.
(__ieee754_gammal_r): Do intermediate computations in
round-to-nearest then adjust overflowing and underflowing results
as needed. Use 1.0L not 1.0f as numerator of division.
* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (gammal_positive): Take
log of X_ADJ not X when adjusting exponent.
(__ieee754_gammal_r): Do intermediate computations in
round-to-nearest then adjust overflowing and underflowing results
as needed. Use 1.0L not 1.0f as numerator of division.
* sysdeps/ieee754/ldbl-96/e_gammal_r.c (gammal_positive): Take log
of X_ADJ not X when adjusting exponent.
(__ieee754_gammal_r): Do intermediate computations in
round-to-nearest then adjust overflowing and underflowing results
as needed. Use 1.0L not 1.0f as numerator of division.
* math/libm-test.inc (tgamma_test_data): Remove one test. Moved
to auto-libm-test-in.
(tgamma_test): Use ALL_RM_TEST.
* math/auto-libm-test-in: Add one test of tgamma. Mark some other
tests of tgamma with spurious-overflow.
* math/auto-libm-test-out: Regenerated.
* math/gen-libm-have-vector-test.sh: Do not check for START.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The ldbl-128 implementation of j1l produces spurious underflow
exceptions for some small arguments, as a result of squaring the
argument. This patch fixes it just to use a linear approximation for
sufficiently small arguments, and then to force an underflow exception
only in the cases where it is required.
Tested for mips64.
[BZ #18612]
* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): For small
arguments, just return 0.5 times the argument, with underflow
forced as needed.
* math/auto-libm-test-in: Add more tests of j1.
* math/auto-libm-test-out: Regenerated.
Similar to various other bugs in this area, j1 and jn implementations
can fail to raise the underflow exception when the internal
computation is exact although the actual function is inexact. This
patch forces the exception in a similar way to other such fixes. (The
ldbl-128 / ldbl-128ibm j1l implementation is different and doesn't
need a change for this until spurious underflows in it are fixed.)
Tested for x86_64, x86, mips64 and powerpc.
[BZ #16559]
* sysdeps/ieee754/dbl-64/e_j1.c: Include <float.h>.
(__ieee754_j1): Force underflow exception for small results.
* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Likewise.
* sysdeps/ieee754/flt-32/e_j1f.c: Include <float.h>.
(__ieee754_j1f): Force underflow exception for small results.
* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
* 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: Include <float.h>.
(__ieee754_j1l): Force underflow exception for small results.
* sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise.
* math/auto-libm-test-in: Add more tests of j1 and jn.
* math/auto-libm-test-out: Regenerated.
Some existing jn tests, if run in non-default rounding modes, produce
errors above those accepted in glibc, which causes problems for moving
tests of jn to use ALL_RM_TEST. This patch makes jn set rounding
to-nearest internally, as was done for yn some time ago, then computes
the appropriate underflowing value for results that underflowed to
zero in to-nearest, and moves the tests to ALL_RM_TEST. It does
nothing about the general inaccuracy of Bessel function
implementations in glibc, though it should make jn more accurate on
average in non-default rounding modes through reduced error
accumulation. The recomputation of results that underflowed to zero
should as a side-effect fix some cases of bug 16559, where jn just
used an exact zero, but that is *not* the goal of this patch and other
cases of that bug remain unfixed.
(Most of the changes in the patch are reindentation to add new scopes
for SET_RESTORE_ROUND*.)
Tested for x86_64, x86, powerpc and mips64.
[BZ #16559]
[BZ #18602]
* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Set
round-to-nearest internally then recompute results that
underflowed to zero in the original rounding mode.
* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
* 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_jnl.c (__ieee754_jnl): Likewise
* math/libm-test.inc (jn_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
Similar to various other bugs in this area, the ldbl-128 expl
implementation does not raise the underflow exception for all
subnormal results, if the scaling down is exact although the actual
result is inexact. This patch fixes this by forcing the exception in
this case (the tests that failed before and pass after the test are
already in the testsuite).
Tested for mips64.
[BZ #18586]
* sysdeps/ieee754/ldbl-128/e_expl.c (__ieee754_expl): Force
underflow exception for small results.
Similar to various other bugs in this area, some sin and sincos
implementations do not raise the underflow exception for subnormal
arguments, when the result is tiny and inexact. This patch forces the
exception in a similar way to previous fixes.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #16526]
[BZ #16538]
* sysdeps/ieee754/dbl-64/s_sin.c: Include <float.h>.
(__sin): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/flt-32/k_sinf.c: Include <float.h>.
(__kernel_sinf): Force underflow exception for arguments with
small absolute value.
* sysdeps/ieee754/ldbl-128/k_sincosl.c: Include <float.h>.
(__kernel_sincosl): Force underflow exception for arguments with
small absolute value.
* sysdeps/ieee754/ldbl-128/k_sinl.c: Include <float.h>.
(__kernel_sinl): Force underflow exception for arguments with
small absolute value.
* sysdeps/ieee754/ldbl-128ibm/k_sincosl.c: Include <float.h>.
(__kernel_sincosl): Force underflow exception for arguments with
small absolute value.
* sysdeps/ieee754/ldbl-128ibm/k_sinl.c: Include <float.h>.
(__kernel_sinl): Force underflow exception for arguments with
small absolute value.
* sysdeps/ieee754/ldbl-96/k_sinl.c: Include <float.h>.
(__kernel_sinl): Force underflow exception for arguments with
small absolute value.
* sysdeps/powerpc/fpu/k_sinf.c: Include <float.h>.
(__kernel_sinf): Force underflow exception for arguments with
small absolute value.
* math/auto-libm-test-in: Add more tests of sin and sincos.
* math/auto-libm-test-out: Regenerated.
Similar to various other bugs in this area, some asinh implementations
do not raise the underflow exception for subnormal arguments, when the
result is tiny and inexact. This patch forces the exception in a
similar way to previous fixes.
Tested for x86_64, x86 and mips64.
[BZ #16350]
* sysdeps/i386/fpu/s_asinh.S (__asinh): Force underflow exception
for arguments with small absolute value.
* sysdeps/i386/fpu/s_asinhf.S (__asinhf): Likewise.
* sysdeps/i386/fpu/s_asinhl.S (__asinhl): Likewise.
* sysdeps/ieee754/dbl-64/s_asinh.c: Include <float.h>.
(__asinh): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/flt-32/s_asinhf.c: Include <float.h>.
(__asinhf): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/ldbl-128/s_asinhl.c: Include <float.h>.
(__asinhl): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c: Include <float.h>.
(__asinhl): Force underflow exception for arguments with small
absolute value.
* sysdeps/ieee754/ldbl-96/s_asinhl.c: Include <float.h>.
(__asinhl): Force underflow exception for arguments with small
absolute value.
* math/auto-libm-test-in: Do not mark underflow exceptions as
possibly missing for bug 16350.
* math/auto-libm-test-out: Regenerated.
The ldbl-128 and ldbl-128ibm implementations of tanl produce
uninitialized variable warnings with -Wuninitialized because of a
variable that is initialized only conditionally, then used under the
same conditions under which it is set. This patch uses DIAG_* macros
to suppress those warnings.
Tested for powerpc and mips64.
* sysdeps/ieee754/ldbl-128/k_tanl.c: Include <libc-internal.h>.
(__kernel_tanl): Ignore uninitialized warnings around use of SIGN.
* sysdeps/ieee754/ldbl-128ibm/k_tanl.c: Include <libc-internal.h>.
(__kernel_tanl): Ignore uninitialized warnings around use of SIGN.
The ldbl-128 and ldbl-128ibm implementations of erfcl produce
uninitialized variable warnings with -Wuninitialized because of switch
statements where in fact one of the cases will always be executed, but
the compiler does not see that these cases cover all possibilities
(and because the reasoning that it does involves inequalities on the
representation of a floating point value leading to a set of possible
values for 8.0 times that value, converted to int, it's highly
nontrivial for the compiler to see that). This patch fixes those
warnings by converting the last case in those switch statements to a
"default" case.
Tested for powerpc and mips64.
* sysdeps/ieee754/ldbl-128/s_erfl.c (__erfcl): Make case 9 in
switch statement into default case.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfcl): Likewise.
The ldbl-128 and ldbl-128ibm implementations of asinl produce
uninitialized variable warnings with -Wuninitialized because the code
for small arguments in fact always returns but the compiler cannot see
this and instead sees that a variable would be uninitialized if the
"if (huge + x > one)" conditional used to force the "inexact"
exception were false.
All the code in libm trying to force "inexact" for functions that are
not exactly defined is suspect and should be removed at some point
given that we now have a clear definition of the accuracy goals for
libm functions which, following C99/C11, does not require anything
about "inexact" for most functions (likewise, the multi-precision code
that tries to give correctly-rounded results, very slowly, for
functions for which the goals clearly do not include correct rounding,
if the faster paths are accurate enough). However, for now this patch
simply changes the code to use math_force_eval, rather than "if", to
ensure the evaluation of the inexact computation.
Tested for powerpc and mips64.
* sysdeps/ieee754/ldbl-128/e_asinl.c (__ieee754_asinl): Don't use
a conditional in forcing "inexact".
* sysdeps/ieee754/ldbl-128ibm/e_asinl.c (__ieee754_asinl):
Likewise.
Similar to various other bugs in this area, some atanh implementations
do not raise the underflow exception for subnormal arguments, when the
result is tiny and inexact. This patch forces the exception in a
similar way to previous fixes. (No change in this regard is needed
for the i386 implementation; special handling to force underflows in
these cases will only be needed there when the spurious underflows,
bug 18049, get fixed.)
Tested for x86_64, x86, powerpc and mips64.
[BZ #16352]
* sysdeps/i386/fpu/e_atanh.S (dbl_min): New object.
(__ieee754_atanh): Force underflow exception for results with
small absolute value.
* sysdeps/i386/fpu/e_atanhf.S (flt_min): New object.
(__ieee754_atanhf): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/dbl-64/e_atanh.c: Include <float.h>.
(__ieee754_atanh): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/flt-32/e_atanhf.c: Include <float.h>.
(__ieee754_atanhf): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/ldbl-128/e_atanhl.c: Include <float.h>.
(__ieee754_atanhl): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c: Include <float.h>.
(__ieee754_atanhl): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/ldbl-96/e_atanhl.c: Include <float.h>.
(__ieee754_atanhl): Force underflow exception for results with
small absolute value.
* math/auto-libm-test-in: Do not allow missing underflow
exceptions from atanh.
* math/auto-libm-test-out: Regenerated.
Similar to various other bugs in this area, some log1p implementations
do not raise the underflow exception for subnormal arguments, when the
result is tiny and inexact. This patch forces the exception in a
similar way to previous fixes. (The ldbl-128ibm implementation
doesn't currently need any change as it already generates this
exception, albeit through code that would generate spurious exceptions
in other cases; special code for this issue will only be needed there
when fixing the spurious exceptions.)
Tested for x86_64, x86, powerpc and mips64.
[BZ #16339]
* sysdeps/i386/fpu/s_log1p.S (dbl_min): New object.
(__log1p): Force underflow exception for results with small
absolute value.
* sysdeps/i386/fpu/s_log1pf.S (flt_min): New object.
(__log1pf): Force underflow exception for results with small
absolute value.
* sysdeps/ieee754/dbl-64/s_log1p.c: Include <float.h>.
(__log1p): Force underflow exception for results with small
absolute value.
* sysdeps/ieee754/flt-32/s_log1pf.c: Include <float.h>.
(__log1pf): Force underflow exception for results with small
absolute value.
* sysdeps/ieee754/ldbl-128/s_log1pl.c: Include <float.h>.
(__log1pl): Force underflow exception for results with small
absolute value.
* math/auto-libm-test-in: Do not allow missing underflow
exceptions from log1p.
* math/auto-libm-test-out: Regenerated.
The implementation of roundl for ldbl-128 involves undefined behavior
for arguments with exponents from 31 to 47 inclusive, from the shift:
u_int64_t i = -1ULL >> (j0 - 48);
For example, on mips64, this means roundl (0xffffffffffff.8p0L)
wrongly returns its argument, which is not an integer. A condition
checking for exponents < 31 should actually be checking for exponents
< 48, and this patch makes it do so. (That condition is for whether
the bit representing 0.5 is in the high 64-bit half of the
floating-point number. The value 31 might have arisen from an
incorrect conversion of the ldbl-96 version to handle ldbl-128.)
This was originally reported as a GCC libquadmath bug
<https://gcc.gnu.org/bugzilla/show_bug.cgi?id=65757>.
Tested for mips64; also tested for x86_64 and x86 to make sure the new
tests pass there.
[BZ #18346]
* sysdeps/ieee754/ldbl-128/s_roundl.c (__roundl): Handle all
exponents less than 48 as cases where high part of mantissa needs
examining to determine whether argument is integral.
* math/libm-test.inc (round_test_data): Add more tests.
According to bug 6792, errno is not set to ERANGE/EDOM
by calling log1p/log1pf/log1pl with x = -1 or x < -1.
This patch adds a wrapper which sets errno in those cases
and returns the value of the existing __log1p function.
The log1p is now an alias to the wrapper function
instead of __log1p.
The files in sysdeps are reflecting these changes.
The ia64 implementation sets errno by itself,
thus the wrapper-file is empty.
The libm-test is adjusted for log1p-tests to check errno.
[BZ #6792]
* math/w_log1p.c: New file.
* math/w_log1pf.c: Likewise.
* math/w_log1pl.c: Likewise.
* math/Makefile (libm-calls): Add w_log1p.
* math/s_log1pl.c (log1pl): Remove weak_alias.
* sysdeps/i386/fpu/s_log1p.S (log1p): Likewise.
* sysdeps/i386/fpu/s_log1pf.S (log1pf): Likewise.
* sysdeps/i386/fpu/s_log1pl.S (log1pl): Likewise.
* sysdeps/x86_64/fpu/s_log1pl.S (log1pl): Likewise.
* sysdeps/ieee754/dbl-64/s_log1p.c (log1p): Likewise.
[NO_LONG_DOUBLE] (log1pl): Likewise.
* sysdeps/ieee754/flt-32/s_log1pf.c (log1pf): Likewise.
* sysdeps/ieee754/ldbl-128/s_log1pl.c (log1pl): Likewise.
* sysdeps/ieee754/ldbl-64-128/s_log1pl.c
(log1p): Remove long_double_symbol.
* sysdeps/ieee754/ldbl-128ibm/s_log1pl.c (log1pl): Likewise.
* sysdeps/ieee754/ldbl-64-128/w_log1pl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/w_log1pl.c: Likewise.
* sysdeps/m68k/m680x0/fpu/s_log1p.c: Define empty weak_alias to
remove weak_alias for corresponding log1p function.
* sysdeps/m68k/m680x0/fpu/s_log1pf.c: Likewise.
* sysdeps/m68k/m680x0/fpu/s_log1pl.c: Likewise.
* sysdeps/ia64/fpu/w_log1p.c: New file.
* sysdeps/ia64/fpu/w_log1pf.c: Likewise.
* sysdeps/ia64/fpu/w_log1pl.c: Likewise.
* math/libm-test.inc (log1p_test_data): Add errno expectations.
The ldbl-128 and ldbl-128ibm implementations of acosl have similar
bugs, using a threshold of 0x1p-57L to determine when they just return
pi/2. Since the result pi/2 - asinl (x) is roughly pi/2 - x for small
x, the relevant cut-off is actually x being < 0.5ulp of 1. This patch
fixes the implementations to use that cut-off and adds tests of small
acos arguments.
Tested for powerpc and mips64. Also tested for x86_64 and x86; no
ulps updates needed.
[BZ #18038]
[BZ #18039]
* sysdeps/ieee754/ldbl-128/e_acosl.c (__ieee754_acosl): Only
return pi/2 for arguments below 0x1p-113L.
* sysdeps/ieee754/ldbl-128ibm/e_acosl.c (__ieee754_acosl): Only
return pi/2 for arguments below 0x1p-106L.
* math/auto-libm-test-in: Add more tests of acos.
* math/auto-libm-test-out: Regenerated.
Similar to various other bugs in this area, some asin implementations
do not raise the underflow exception for subnormal arguments, when the
result is tiny and inexact. This patch forces the exception in a
similar way to previous fixes.
Tested for x86_64, x86, powerpc and mips64.
[BZ #16351]
* sysdeps/i386/fpu/e_asin.S (dbl_min): New object.
(MO): New macro.
(__ieee754_asin): Force underflow exception for results with small
absolute value.
* sysdeps/i386/fpu/e_asinf.S (flt_min): New object.
(MO): New macro.
(__ieee754_asinf): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/dbl-64/e_asin.c: Include <float.h> and <math.h>.
(__ieee754_asin): Force underflow exception for results with small
absolute value.
* sysdeps/ieee754/flt-32/e_asinf.c: Include <float.h>.
(__ieee754_asinf): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/ldbl-128/e_asinl.c: Include <float.h>.
(__ieee754_asinl): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/ldbl-128ibm/e_asinl.c: Include <float.h>.
(__ieee754_asinl): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/ldbl-96/e_asinl.c: Include <float.h>.
(__ieee754_asinl): Force underflow exception for results with
small absolute value.
* sysdeps/x86_64/fpu/multiarch/e_asin.c [HAVE_FMA4_SUPPORT]:
Include <math.h>.
* math/auto-libm-test-in: Do not mark underflow exceptions as
possibly missing for bug 16351.
* math/auto-libm-test-out: Regenerated.
This patch fixes bug 15319, missing underflows from atan / atan2 when
the result of atan is very close to its small argument (or that of
atan2 is very close to the ratio of its arguments, which may be an
exact division).
The usual approach of doing an underflowing computation if the
computed result is subnormal is followed. For 32-bit x86, there are
extra complications: the inline __ieee754_atan2 in bits/mathinline.h
needs to be disabled for float and double because other libm functions
using it generally rely on getting proper underflow exceptions from
it, while the out-of-line functions have to remove excess range and
precision from the underflowing result so as to return an exact 0 in
the case where errno should be set for underflow to 0. (The failures
I saw without that are similar to those Carlos reported for other
functions, where I haven't seen a response to
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>
confirming if my diagnosis is correct. Arguably all libm functions
with float and double returns should remove excess range and
precision, but that's a separate matter.)
The x86_64 long double case reported in a comment in bug 15319 is not
a bug (it's an argument of LDBL_MIN, and x86_64 is an after-rounding
architecture so the correct IEEE result is not to raise underflow in
the given rounding mode, in addition to treating the result as an
exact LDBL_MIN being within the newly clarified documentation of
accuracy goals). I'm presuming that the fpatan instruction can be
trusted to raise appropriate exceptions when the (long double) result
underflows (after rounding) and so no changes are needed for x86 /
x86_64 long double functions here; empirically this is the case for
the cases covered in the testsuite, on my system.
Tested for x86_64, x86, powerpc and mips64. Only 32-bit x86 needs
ulps updates (for the changes to inlines meaning some functions no
longer get excess precision from their __ieee754_atan2* calls).
[BZ #15319]
* sysdeps/i386/fpu/e_atan2.S (dbl_min): New object.
(MO): New macro.
(__ieee754_atan2): For results with small absolute value, force
underflow exception and remove excess range and precision from
return value.
* sysdeps/i386/fpu/e_atan2f.S (flt_min): New object.
(MO): New macro.
(__ieee754_atan2f): For results with small absolute value, force
underflow exception and remove excess range and precision from
return value.
* sysdeps/i386/fpu/s_atan.S (dbl_min): New object.
(MO): New macro.
(__atan): For results with small absolute value, force underflow
exception and remove excess range and precision from return value.
* sysdeps/i386/fpu/s_atanf.S (flt_min): New object.
(MO): New macro.
(__atanf): For results with small absolute value, force underflow
exception and remove excess range and precision from return value.
* sysdeps/ieee754/dbl-64/e_atan2.c: Include <float.h> and
<math.h>.
(__ieee754_atan2): Force underflow exception for results with
small absolute value.
* sysdeps/ieee754/dbl-64/s_atan.c: Include <float.h> and
<math_private.h>.
(atan): Force underflow exception for results with small absolute
value.
* sysdeps/ieee754/flt-32/s_atanf.c: Include <float.h>.
(__atanf): Force underflow exception for results with small
absolute value.
* sysdeps/ieee754/ldbl-128/s_atanl.c: Include <float.h> and
<math.h>.
(__atanl): Force underflow exception for results with small
absolute value.
* sysdeps/ieee754/ldbl-128ibm/s_atanl.c: Include <float.h>.
(__atanl): Force underflow exception for results with small
absolute value.
* sysdeps/x86/fpu/bits/mathinline.h
[!__SSE2_MATH__ && !__x86_64__ && __LIBC_INTERNAL_MATH_INLINES]
(__ieee754_atan2): Only define inline for long double.
* sysdeps/x86_64/fpu/multiarch/e_atan2.c
[HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Include <math.h>.
* math/auto-libm-test-in: Do not mark underflow exceptions as
possibly missing for bug 15319. Add more tests of atan2.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (casin_test_data): Do not mark underflow
exceptions as possibly missing for bug 15319.
(casinh_test_data): Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Update.
Various remquo implementations produce a zero remainder with the wrong
sign (a zero remainder should always have the sign of the first
argument, as specified in IEEE 754) in round-downward mode, resulting
from the sign of 0 - 0. This patch checks for zero results and fixes
their sign accordingly.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #17987]
* sysdeps/ieee754/dbl-64/s_remquo.c (__remquo): Ensure sign of
zero result does not depend on the sign resulting from
subtraction.
* sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c (__remquo):
Likewise.
* sysdeps/ieee754/flt-32/s_remquof.c (__remquof): Likewise.
* sysdeps/ieee754/ldbl-128/s_remquol.c (__remquol): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_remquol.c (__remquol): Likewise.
* sysdeps/ieee754/ldbl-96/s_remquol.c (__remquol): Likewise.
* math/libm-test.inc (remquo_test_data): Add more tests.
Various remquo implementations, when computing the last three bits of
the quotient, have spurious overflows when 4 times the second argument
to remquo overflows. These overflows can in turn cause bad results in
rounding modes where that overflow results in a finite value. This
patch adds tests to avoid the problem multiplications in cases where
they would overflow, similar to those that control an earlier
multiplication by 8.
Tested for x86_64, x86, mips64 and powerpc.
[BZ #17978]
* sysdeps/ieee754/dbl-64/s_remquo.c (__remquo): Do not form
products 4 * y and 2 * y where those would overflow.
* sysdeps/ieee754/dbl-64/wordsize-64/s_remquo.c (__remquo):
Likewise.
* sysdeps/ieee754/flt-32/s_remquof.c (__remquof): Likewise.
* sysdeps/ieee754/ldbl-128/s_remquol.c (__remquol): Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_remquol.c (__remquol): Likewise.
* sysdeps/ieee754/ldbl-96/s_remquol.c (__remquol): Likewise.
* math/libm-test.inc (remquo_test_data): Add more tests.
This patch makes sincos set errno to EDOM when passed an infinity,
similarly to sin and cos.
Tested for x86_64, x86, powerpc and mips64. I don't know if the
architecture-specific implementations for ia64 and m68k might need
corresponding fixes.
2015-02-11 Joseph Myers <joseph@codesourcery.com>
[BZ #15467]
* sysdeps/ieee754/dbl-64/s_sincos.c: Include <errno.h>.
(__sincos): Set errno to EDOM for infinite argument.
* sysdeps/ieee754/flt-32/s_sincosf.c: Include <errno.h>.
(SINCOSF_FUNC): Set errno to EDOM for infinite argument.
* sysdeps/ieee754/ldbl-128/s_sincosl.c: Include <errno.h>.
(__sincosl): Set errno to EDOM for infinite argument.
* sysdeps/ieee754/ldbl-128ibm/s_sincosl.c: Include <errno.h>.
(__sincosl): Set errno to EDOM for infinite argument.
* sysdeps/ieee754/ldbl-96/s_sincosl.c: Include <errno.h>.
(__sincosl): Set errno to EDOM for infinite argument.
* math/libm-test.inc (sincos_test_data): Test errno setting.
ldbl-128ibm uses ldbl-128 e_lgammal_r implementation as is, however some
constants definitions overflows for IBM long double range. This patch
suppress the compiler warnings until the ldbl-128ibm implementation is
fixed.
This patch fixes spurious underflows from ldbl-128 expm1l, as reported
in <https://sourceware.org/ml/libc-alpha/2014-06/msg00835.html> and
exposed by the tests added for such a bug in the x86 / x86-64
version. The bug and fix are essentially the same, so no separate bug
is filed in Bugzilla.
Tested for mips64.
[BZ #16539]
* sysdeps/ieee754/ldbl-128/s_expm1l.c: Include <float.h>.
(__expm1l): Return argument unchanged when small but not
subnormal.
This patch fixes bug 17097, ldbl-128 powl producing overflowing /
underflowing results with positive sign when the result should have
been negative. This was shown up by the tests in non-default rounding
modes added by my patch for bug 16315, but isn't actually limited to
non-default rounding modes: rather, when rounding to nearest the
wrappers produced a result with the correct sign and so always hid the
bug unless -lieee was used to disable the wrappers. The problem is
that in the cases where Y is large enough that the result overflows or
underflows for X not very close to 1, but not large enough to overflow
or underflow for all X != +/- 1 (in the latter case Y is always an
even integer), a positive overflowing / underflowing result is always
returned, rather than one with the correct sign. This patch moves the
relevant part of computation of the sign earlier and returns a result
of the correct sign.
Tested for mips64.
[BZ #17097]
* sysdeps/ieee754/ldbl-128/e_powl.c (__ieee754_powl): Return
result with correct sign in case of exponents that produce
overflow except for X very close to 1.
This patch fixes bugs 16561 and 16562, bad results of yn in overflow
cases in non-default rounding modes, both because an intermediate
overflow in the recurrence does not get detected if the result is not
an infinity and because an overflowing result may occur in the wrong
sign. The fix is to set FE_TONEAREST mode internally for the parts of
the function where such overflows can occur (which includes the call
to y1 - where yn is used to compute a Bessel function of order -1,
negating the result of y1 isn't correct for overflowing results in
directed rounding modes) and then compute an overflowing value in the
original rounding mode if the to-nearest result was an infinity.
Tested x86_64 and x86 and ulps updated accordingly. Also tested for
mips64 and powerpc32 to test the ldbl-128 and ldbl-128ibm changes.
(The tests for these bugs were added in my previous y1 patch, so the
only thing this patch has to do with the testsuite is enable yn
testing in all rounding modes.)
[BZ #16561]
[BZ #16562]
* sysdeps/ieee754/dbl-64/e_jn.c: Include <float.h>.
(__ieee754_yn): Set FE_TONEAREST mode internally and then
recompute overflowing results in original rounding mode.
* sysdeps/ieee754/flt-32/e_jnf.c: Include <float.h>.
(__ieee754_ynf): Set FE_TONEAREST mode internally and then
recompute overflowing results in original rounding mode.
* sysdeps/ieee754/ldbl-128/e_jnl.c: Include <float.h>.
(__ieee754_ynl): Set FE_TONEAREST mode internally and then
recompute overflowing results in original rounding mode.
* sysdeps/ieee754/ldbl-128ibm/e_jnl.c: Include <float.h>.
(__ieee754_ynl): Set FE_TONEAREST mode internally and then
recompute overflowing results in original rounding mode.
* sysdeps/ieee754/ldbl-96/e_jnl.c: Include <float.h>.
(__ieee754_ynl): Set FE_TONEAREST mode internally and then
recompute overflowing results in original rounding mode.
* sysdeps/i386/fpu/fenv_private.h [!__SSE2_MATH__]
(libc_feholdsetround_ctx): New macro.
* math/libm-test.inc (yn_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps : Likewise.
This patch fixes spurious underflows from exp10 for arguments near 0
(part of bug 16560; that bug also includes spurious underflows from
exp2, which are not fixed by this patch). The problem is underflows
in the internal computation converting the exp10 argument to arguments
for exp (with extra precision), and the fix is simply to return 1
early for arguments near enough to 0 (just as arguments with large
enough magnitude have their own overflow / underflow logic at the
start of the function).
Tested x86_64 and x86 and ulps updated accordingly; also tested for
powerpc32 and mips64 to validate the ldbl-128ibm and ldbl-128 changes.
[BZ #16560]
* sysdeps/ieee754/dbl-64/e_exp10.c (__ieee754_exp10): Return 1 for
arguments close to 0.
* sysdeps/ieee754/ldbl-128/e_exp10l.c (__ieee754_exp10l):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/e_exp10l.c (__ieee754_exp10l):
Likewise.
* math/auto-libm-test-in: Add more tests of exp10.
* math/auto-libm-test-out: Regenerated.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
This patch fixes bug 16287, spurious underflows from ldbl-128 erfl
arising from it calling erfcl for arguments with absolute value at
least 1.0, although for large positive arguments erfcl correctly
underflows but erfl shouldn't. The fix is simply to avoid calling
erfcl, and just return 1, for arguments above a cut-off large enough
that erfl correctly rounds to-nearest as 1 but not so large that erfcl
underflows.
Tested mips64. Also tested x86_64 and x86 to confirm the new tests
(taken from the tests of erfc) don't cause any problems there; no ulps
updates needed.
[BZ #16287]
* sysdeps/ieee754/ldbl-128/s_erfl.c (__erfl): Return 1 without
calling __erfcl for arguments at least 16.
* math/auto-libm-test-in: Add more tests of erf.
* math/auto-libm-test-out: Regenerated.
This patch fixes bug 16354, spurious underflows from cosh when a tiny
argument is passed to expm1 and expm1 correctly underflows although
the final result of cosh should be 1. As noted in that bug, some
cases are latent because of expm1 implementations not raising
underflow (bug 16353), but all the implementations are fixed
similarly. They already contained checks for tiny arguments, but the
checks were too late to avoid underflow from expm1 (although they
would avoid underflow from subsequent squaring of the result of
expm1); they are moved before the expm1 calls.
The thresholds used for considering arguments tiny are not
particularly consistent in how they relate to the precision of the
floating-point format in question. They are, however, all sufficient
to ensure that the round-to-nearest result of cosh is indeed 1 below
the threshold (although sometimes they are smaller than necessary).
But the previous logic did not return 1, but the previously computed 1
+ expm1(abs(x)) value. And the thresholds in the ldbl-128 and
ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code
instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for
that value to be 1. So by moving the test for tiny arguments, and
consequently returning 1 directly now the expm1 value hasn't been
computed by that point, this patch also fixes bug 17061, the (large
number of ulps) inaccuracy for small arguments in those
implementations. Tests for that bug are duly added.
Tested x86_64 and x86 and ulps updated accordingly. Also tested for
mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes.
[BZ #16354]
[BZ #17061]
* sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for
small arguments before calling __expm1.
* sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for
small arguments before calling __expm1f.
* sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for
small arguments before calling __expm1l.
* sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl):
Likewise.
* sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise.
* math/auto-libm-test-in: Add more cosh tests. Do not allow
spurious underflow for some cosh tests.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
This patch fixes bug 17050, missing errno setting for y1 overflow (for
small positive arguments). An appropriate check is added for overflow
directly in the __ieee754_y1 implementation, similar to the check
present for yn (doing it there rather than in the wrapper also avoids
yn needing to repeat the check when called for order 1 or -1 and it
uses __ieee754_y1).
Tested x86_64 and x86; no ulps update needed. Also tested for mips64
to verify the ldbl-128 fix (the ldbl-128ibm code just #includes the
ldbl-128 file).
[BZ #17050]
* sysdeps/ieee754/dbl-64/e_j1.c: Include <errno.h>.
(__ieee754_y1): Set errno if return value overflows.
* sysdeps/ieee754/flt-32/e_j1f.c: Include <errno.h>.
(__ieee754_y1f): Set errno if return value overflows.
* sysdeps/ieee754/ldbl-128/e_j1l.c: Include <errno.h>.
(__ieee754_y1l): Set errno if return value overflows.
* sysdeps/ieee754/ldbl-96/e_j1l.c: Include <errno.h>.
(__ieee754_y1l): Set errno if return value overflows.
* math/auto-libm-test-in: Add more tests of y0, y1 and yn.
* math/auto-libm-test-out: Regenerated.
Errno is not set and the testcases will fail.
Now the scalbln-aliases are removed in i386/m68
and the wrappers are used when calling the scalbln-functions.
On ia64 only scalblnf has its own implementation.
For scalbln and scalblnl the ieee754/dbl-64 and ieee754/ldbl-96 are used, thus
the wrappers are needed, too.
As with other issues of this kind, bug 17042 is log2 (1) wrongly
returning -0 instead of +0 in round-downward mode because of
implementations effectively in terms of log1p (x - 1). This patch
fixes the issue in the same way used for log and log10.
Tested x86_64 and x86 and ulps updated accordingly. Also tested for
mips64 to confirm a fix was needed for ldbl-128 and to validate that
fix (also applied to ldbl-128ibm since that version of log2l is
essentially the same as the ldbl-128 one).
[BZ #17042]
* sysdeps/i386/fpu/e_log2.S (__ieee754_log2): Take absolete value
when x - 1 is zero.
* sysdeps/i386/fpu/e_log2f.S (__ieee754_log2f): Likewise.
* sysdeps/i386/fpu/e_log2l.S (__ieee754_log2l): Likewise.
* sysdeps/ieee754/ldbl-128/e_log2l.c (__ieee754_log2l): Return
0.0L for an argument of 1.0L.
* sysdeps/ieee754/ldbl-128ibm/e_log2l.c (__ieee754_log2l):
Likewise.
* sysdeps/x86_64/fpu/e_log2l.S (__ieee754_log2l): Take absolute
value when x - 1 is zero.
* math/libm-test.inc (log2_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
As with various other issues of this kind, bug 16977 is log10 (1)
wrongly returning -0 rather than +0 in round-downward mode because of
an implementation effectively in terms of log1p (x - 1). This patch
fixes the issue in the same way used for log.
Tested x86_64 and x86 and ulps updated accordingly. Also tested for
mips64 to confirm a fix was needed for ldbl-128 and to validate that
fix (also applied to ldbl-128ibm since that version of logl is
essentially the same as the ldbl-128 one).
[BZ #16977]
* sysdeps/i386/fpu/e_log10.S (__ieee754_log10): Take absolute
value when x - 1 is zero.
* sysdeps/i386/fpu/e_log10f.S (__ieee754_log10f): Likewise.
* sysdeps/i386/fpu/e_log10l.S (__ieee754_log10l): Likewise.
* sysdeps/ieee754/ldbl-128/e_log10l.c (__ieee754_log10l): Return
0.0L for an argument of 1.0L.
* sysdeps/ieee754/ldbl-128ibm/e_log10l.c (__ieee754_log10l):
Likewise.
* sysdeps/x86_64/fpu/e_log10l.S (__ieee754_log10l): Take absolute
value when x - 1 is zero.
* math/libm-test.inc (log10_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
Bug 16564 is spurious overflow of log1pl (LDBL_MAX) in FE_UPWARD mode,
resulting from log1pl adding 1 to its argument (for arguments not
close to 0), which overflows in that mode. This patch fixes this by
avoiding adding 1 to large arguments (precisely what counts as large
depends on the floating-point format).
Tested x86_64 and x86, and spot-checked log1pl tests on mips64 and
powerpc64.
[BZ #16564]
* sysdeps/i386/fpu/s_log1pl.S (__log1pl): Do not add 1 to positive
arguments with exponent 65 or above.
* sysdeps/ieee754/ldbl-128/s_log1pl.c (__log1pl): Do not add 1 to
arguments 0x1p113L or above.
* sysdeps/ieee754/ldbl-128ibm/s_log1pl.c (__log1pl): Do not add 1
to arguments 0x1p107L or above.
* sysdeps/x86_64/fpu/s_log1pl.S (__log1pl): Do not add 1 to
positive arguments with exponent 65 or above.
* math/auto-libm-test-in: Add more tests of log1p.
* math/auto-libm-test-out: Regenerated.
Bug 16516 reports spurious underflows from erf (for all floating-point
types), when the result is close to underflowing but does not actually
underflow.
erf (x) is about (2/sqrt(pi))*x for x close to 0, so there are
subnormal arguments for which it does not underflow. The various
implementations do (x + efx*x) (for efx = 2/sqrt(pi) - 1), for greater
accuracy than if just using a single multiplication by an
approximation to 2/sqrt(pi) (effectively, this way there are a few
more bits in the approximation to 2/sqrt(pi)). This can introduce
underflows when efx*x underflows even though the final result does
not, so a scaled calculation with 8*efx is done in these cases - but 8
is not a big enough scale factor to avoid all such underflows. 16 is
(any underflows with a scale factor of 16 would only occur when the
final result underflows), so this patch changes the code to use that
factor. Rather than recomputing all the values of the efx8 variable,
it is removed, leaving it to the compiler's constant folding to
compute 16*efx. As such scaling can also lose underflows when the
final scaling down happens to be exact, appropriate checks are added
to ensure underflow exceptions occur when required in such cases.
Tested x86_64 and x86; no ulps updates needed. Also spot-checked for
powerpc32 and mips64 to verify the changes to the ldbl-128ibm and
ldbl-128 implementations.
[BZ #16516]
* sysdeps/ieee754/dbl-64/s_erf.c (efx8): Remove variable.
(__erf): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/flt-32/s_erff.c (efx8): Remove variable.
(__erff): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/ldbl-128/s_erfl.c: Include <float.h>.
(efx8): Remove variable.
(__erfl): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c: Include <float.h>.
(efx8): Remove variable.
(__erfl): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* sysdeps/ieee754/ldbl-96/s_erfl.c: Include <float.h>.
(efx8): Remove variable.
(__erfl): Scale by 16 instead of 8 in potentially underflowing
case. Ensure exception if result actually underflows.
* math/auto-libm-test-in: Add more tests of erf.
* math/auto-libm-test-out: Regenerated.
According to ISO C Annex F, log (1) should be +0 in all rounding
modes, but some implementations in glibc wrongly return -0 in
round-downward mode (mapping to log1p (x - 1) is problematic because 1
- 1 is -0 in round-downward mode, and log1p (-0) is -0). This patch
fixes this. (It helps with some implementations of other functions
such as acosh, log2 and log10 that call out to log, but not enough to
enable all-rounding-modes testing for those functions without further
fixes to other implementations of them.)
Tested x86_64 and x86 and ulps updated accordingly, and did spot tests
for mips64 for the ldbl-128 fix, and i586 for the sysdeps/i386/fpu
implementations shadowed by those in sysdeps/i386/i686/fpu.
[BZ #16731]
* sysdeps/i386/fpu/e_log.S (__ieee754_log): Take absolute value
when x - 1 is zero.
* sysdeps/i386/fpu/e_logf.S (__ieee754_logf): Likewise.
* sysdeps/i386/fpu/e_logl.S (__ieee754_logl): Likewise.
* sysdeps/i386/i686/fpu/e_logl.S (__ieee754_logl): Likewise.
* sysdeps/ieee754/dbl-64/e_log.c (__ieee754_log): Return +0 when
argument is 1.
* sysdeps/ieee754/ldbl-128/e_logl.c (__ieee754_logl): Likewise.
* sysdeps/x86_64/fpu/e_logl.S: Take absolute value when x - 1 is
zero.
* math/libm-test.inc (log_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
ISO C requires the result of nextafter to be independent of the
rounding mode, even when underflow or overflow occurs. This patch
fixes the bug in various nextafter implementations that, having done
an overflowing computation to force an overflow exception (correct),
they then return the result of that computation rather than an
infinity computed some other way (incorrect, when the overflowing
result of arithmetic with that sign and rounding mode is finite but
the correct result is infinite) - generally by falling through to
existing code to return a value that in fact is correct for this case
(but was computed by an integer increment and so without generating
the exceptions required). Having fixed the bug, the previously
deferred conversion of nextafter testing in libm-test.inc to
ALL_RM_TEST is also included.
Tested x86_64 and x86; also spot-checked results of nextafter tests
for powerpc32 and mips64 to test the ldbl-128ibm and ldbl-128
changes. (The m68k change is untested.)
[BZ #16677]
* math/s_nextafter.c (__nextafter): Do not return value from
overflowing computation.
* sysdeps/i386/fpu/s_nextafterl.c (__nextafterl): Likewise.
* sysdeps/ieee754/flt-32/s_nextafterf.c (__nextafterf): Likewise.
* sysdeps/ieee754/ldbl-128/s_nextafterl.c (__nextafterl):
Likewise.
* sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c (__nextafterl):
Likewise.
* sysdeps/m68k/m680x0/fpu/s_nextafterl.c (__nextafterl): Likewise.
* math/libm-test.inc (nextafter_test): Use ALL_RM_TEST.
This patch fixes bug 16400, spurious underflow exceptions for ldbl-128
/ ldbl-128ibm lgammal with small positive arguments, by just using
-__logl (x) as the result in the problem cases (similar to the
previous fix for problems with small negative arguments).
Tested powerpc32, and also tested on mips64 that this does not require
ulps regeneration for the ldbl-128 case.
* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
Return -__logl (x) for small positive arguments without evaluating
a polynomial.
This patch fixes bug 16337, ldbl-128 lgammal spurious overflows for
small negative arguments (the arguments in question are already in the
testsuite). The implementation uses the reflection formula to compute
lgamma of negative x from lgamma of -x, effectively resulting in a
calculation -log(x^2) + log(-x); cancellation isn't problematic in
this case (bugs for problematic cancellation in lgamma are 2542, 2543,
2558), but the x^2 calculation can underflow (in which case there is
spurious logic to return an overflowing value - lgamma can only ever
correctly overflow for large positive arguments, though tgamma can
overflow for small arguments of either sign as well as large positive
arguments). The fix is simply to calculate the result directly with
logl when the argument is a small enough negative number.
Tested mips64.
* sysdeps/ieee754/ldbl-128/e_lgammal_r.c (__ieee754_lgammal_r):
Calculate results for small negative arguments directly rather
than using reflection formula with special underflow handling.
This patch fixes bug 16338, ldbl-128 logl not handling subnormals
(with consequent inaccuracy for lgammal as well). The fix is simply
to use __frexpl when determining the exponent, as done already in
log2l and log10l. Given the lack of testing of small arguments to any
of the log* functions, appropriate tests are added for all of them.
Tested x86_64 and x86 and ulps updated accordingly, and spot tests
also run for mips64 to confirm the ldbl-128 fix.
Note that while this fixes lgammal inaccuracy for small positive
arguments, I suspect that there will still be problems with spurious
underflows in that case.
* sysdeps/ieee754/ldbl-128/e_logl.c (__ieee754_logl): Use __frexpl
to determine exponent and adjust argument to have exponent of -1.
* math/auto-libm-test-in: Add more tests of log, log10, log1p and
log2.
* math/auto-libm-test-out: Regenerated.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
