This patch adds some randomly-generated tests of lgamma that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* 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.
This patch adds some randomly-generated tests of log, log10, log1p and
log2 that are observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of log, log10, log2 and
log1p.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of exp, exp10, exp2 and
expm1 that are observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of exp, exp10, exp2 and
expm1.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of erf and erfc that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of erf and erfc.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of csqrt that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of csqrt.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some further randomly-generated tests of cosh and sinh
that are observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of cosh and sinh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of clog and clog10 that
are observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* 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.
This patch adds some randomly-generated tests of atanh that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of atanh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of atan that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of atan.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of cbrt that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of cbrt.
* math/auto-libm-test-out: Regenerated.
* sysdeps/x86_64/fpu/libm-test-ulps: Update.
This patch adds some randomly-generated tests of cabs that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of cabs.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The dbl-64 implementation of atan2 does computations that expect to
run in round-to-nearest mode, and in other modes the errors can
accumulate to more than the maximum accepted 9ulp. This patch makes
it use FE_TONEAREST internally, similar to other functions with such
issues. Tests that previously produced large errors are added for
atan2 and the closely related carg, clog and clog10 functions.
Tested for x86_64 and x86 and ulps updated accordingly.
[BZ #18210]
[BZ #18211]
* sysdeps/ieee754/dbl-64/e_atan2.c: Include <fenv.h>.
(__ieee754_atan2): Set FE_TONEAREST mode for internal
computations.
* math/auto-libm-test-in: Add more tests of atan2, carg, 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 dbl-64 implementation of atan does computations that expect to run
in round-to-nearest mode, and in other modes the errors can accumulate
to more than the maximum accepted 9ulp. This patch makes it use
FE_TONEAREST internally, similar to other functions with such issues.
Tested for x86_64 and x86; no ulps updates needed.
[BZ #18197]
* sysdeps/ieee754/dbl-64/s_atan.c: Include <fenv.h>.
(atan): Set FE_TONEAREST mode for internal computations.
* math/auto-libm-test-in: Add more tests of atan.
* math/auto-libm-test-out: Regenerated.
This patch adds some randomly-generated tests of acosh, asinh and
atanh that are observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of acosh, asinh and
atanh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds a randomly-generated test of asin that is observed to
increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add another test of asin.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of asin that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of asin.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of acos that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of acos.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of expm1 that are
observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of expm1.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch adds some randomly-generated tests of cosh and sinh that
are observed to increase ulps on x86_64.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of cosh and sinh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
In testing for x86_64 on an AMD processor, I observed libm test
failures of the form:
testing long double (without inline functions)
Failure: Test: log2_downward (0x2.b7e151628aed4p+0)
Result:
is: 1.44269504088896356633e+00 0xb.8aa3b295c17f67600000p-3
should be: 1.44269504088896356622e+00 0xb.8aa3b295c17f67500000p-3
difference: 1.08420217248550443400e-19 0x8.00000000000000000000p-66
ulp : 1.0000
max.ulp : 0.0000
Maximal error of `log2_downward'
is : 1 ulp
accepted: 0 ulp
These issues arise because the maximum ulps when regenerating on one
processor are not the same as on another processor, so regeneration on
several processors may be needed when updating libm-test-ulps to avoid
failures for some users testing glibc - but such regeneration on
multiple processors is inconvenient. Causes can be: on x86 and, for
x86_64, for long double, variation in results of x87 instructions for
transcendental operations between processors; on x86, variation in
compiler excess precision between compiler versions and
configurations; on any processor where the compiler may contract
expressions using fused multiply-add, variation in what contraction
occurs.
Although it's hard to be sure libm-test-ulps covers all ulps that may
be seen in any configuration for the given architecture, in practice
it helps simply to add wider test coverage to make it more likely
that, when testing on one processor, the ulps seen are the biggest
that can be seen for that function on that processor, and hopefully
they are also the biggest that can be seen for that function in other
configurations for that architecture. Thus, this patch adds some
tests of log2 that increase the ulps I see on x86_64 on an Intel
processor, so that hopefully future from-scratch regenerations on that
processor will produce ulps big enough not to have errors from testing
on AMD processors. These tests were found by randomly generating
inputs and seeing what produced ulps larger than those currently in
libm-test-ulps. Of course such increases also improve the accuracy of
the empirical table of known ulps generated from libm-test-ulps files
that goes in the manual.
Tested for x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add more tests of log2.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The threshold in ldbl-96 atanhl for when to return the argument,
0x1p-28, is a bit too big, and that in ldbl-128ibm atanhl is much too
big (the relevant condition being x^3/3 being < 0.5ulp of x),
resulting in errors a bit above the limits of those considered
acceptable in glibc in the ldbl-96 case, and in large errors in the
ldbl-128ibm case. This patch changes those implementations to use
more appropriate thresholds and adds tests around the thresholds for
various formats.
Tested for x86_64, x86 and powerpc. x86_64 and x86 ulps updated
accordingly.
[BZ #18046]
[BZ #18047]
* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Use
0x1p-56L as threshold for just returning the argument.
* sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Use
0x1p-32L as threshold for just returning the argument.
* math/auto-libm-test-in: Add more tests of atanh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulp: Likewise.
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.
The ldbl-128ibm implementation of asinhl uses cut-offs of 0x1p28 and
0x1p-29 to determine when to use simpler formulas that avoid possible
overflow / underflow. Both those cut-offs are inappropriate for this
format, resulting in large errors. This patch changes the code to use
more appropriate cut-offs of 0x1p56 and 0x1p-56, adding tests around
the cut-offs for various floating-point formats.
Tested for powerpc. Also tested for x86_64 and x86 and updated ulps.
[BZ #18020]
* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Use 2**56 and
2**-56 not 2**28 and 2**-29 as thresholds for simpler formulas.
* math/auto-libm-test-in: Add more tests of asinh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The ldbl-128ibm implementation of acoshl uses a cut-off of 0x1p28 to
determine when to use log(x) + log(2) as a formula. That cut-off is
too small for this format, resulting in large errors. This patch
changes it to a more appropriate cut-off of 0x1p56, adding tests
around the cut-offs for various floating-point formats.
Tested for powerpc. Also tested for x86_64 and x86 and updated ulps.
[BZ #18019]
* sysdeps/ieee754/ldbl-128ibm/e_acoshl.c (__ieee754_acoshl): Use
2**56 not 2**28 as threshold for log (2x) formula.
* math/auto-libm-test-in: Add more tests of acosh.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
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.
This patch fixes the remaining part of bug 16560, spurious underflows
from exp2 of arguments close to 0 (when the result is close to 1, so
should not underflow), by just using 1+x instead of a more complicated
calculation when the argument is sufficiently small.
Tested for x86_64, x86 and mips64.
[BZ #16560]
* math/e_exp2l.c [LDBL_MANT_DIG == 106] (LDBL_EPSILON): Undefine
and redefine.
(__ieee754_exp2l): Do not multiply small fractional parts by
M_LN2l.
* sysdeps/i386/fpu/e_exp2l.S (__ieee754_exp2l): Just add 1 to
small argument.
* 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 (__ieee754_exp2l): Likewise.
* math/auto-libm-test-in: Add more tests of exp2.
* math/auto-libm-test-out: Regenerated.
soft-fp's _FP_FMA fails to set the result's exponent for cases where
the result of the multiplication is 0, yielding incorrect (arbitrary,
depending on uninitialized values) results for those cases. This
affects libm for architectures using soft-fp to implement fma. This
patch adds the exponent setting and tests for this case.
Tested for ARM soft-float (which uses soft-fp fma), x86_64 and x86 (to
verify not introducing new libm test failures there).
(This bug showed up in testing my patch to move the Linux kernel to
current soft-fp. math/Makefile has "override CFLAGS +=
-Wno-uninitialized" which would have stopped compiler warnings from
showing up this problem, although I wouldn't be surprised if removing
that shows spurious warnings from this code, if the compiler fails to
follow that various cases where the exponent is uninitialized don't
need it initialized because the class is set to a value meaning the
uninitialized exponent isn't used.)
[BZ #17932]
* soft-fp/op-common.h (_FP_FMA): Set exponent of result in case
where multiplication results in zero and third argument is finite
and nonzero.
* math/auto-libm-test-in: Add more tests of fma.
* math/auto-libm-test-out: Regenerated.
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 16539, spurious underflow exceptions from x86 /
x86-64 expm1l. The problem is that the computation of a base-2
exponent with extra precision involves spurious underflows for
arguments that are small but not subnormal, so a check is added to
just return the argument in those cases. (If the argument *is*
subnormal, underflowing is correct and the existing code will always
underflow, so it suffices to keep using the existing code in that
case; some expm1 implementations have a bug (bug 16353) with missing
underflow exceptions, but I don't think there's such a bug in this
particular version.)
Tested x86_64 and x86; no ulps updates needed.
(auto-libm-test-out diffs omitted below.)
[BZ #16539]
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Just
return the argument for normal arguments with exponent below -64.
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
Likewise.
* math/auto-libm-test-in: Add another test of expm1.
* math/auto-libm-test-out: Regenerated.
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.
This patch enables testing of cpow in all rounding modes using
ALL_RM_TEST. There were two reasons this was previously deferred:
* MPC has complicated rounding-mode-dependent rules for the signs of
exact zero real or imaginary parts in the result of mpc_pow. Annex
G does not impose any such requirements and I don't think glibc
should try to implement any particular logic here. This patch adds
support for gen-auto-libm-tests passing the IGNORE_ZERO_INF_SIGN
flag to libm-test.inc.
* Error accumulations in some tests in non-default rounding modes
exceed the maximum error permitted in libm-test.inc. This patch
marks the problem tests with xfail-rounding. (It might be possible
to reduce the accumulations a bit by using round-to-nearest when
cpow calls clog, but I don't think there's much point; the
implementation approach for cpow is fundamentally deficient, as
discussed in the existing bug for cpow inaccuracy which can
reasonably be considered to cover these less-inaccurate cases as
well. It's possible that the test "cpow 2 0 10 0" will also need
xfail-rounding on some platforms.)
Tested x86_64 and x86 and ulps updated accordingly.
* math/gen-auto-libm-tests.c: Document use of
ignore-zero-inf-sign.
(input_flag_type): Add value flag_ignore_zero_inf_sign.
(input_flags): Add ignore-zero-inf-sign.
(output_for_one_input_case): Handle flag_ignore_zero_inf_sign.
* math/gen-libm-test.pl (generate_testfile): Handle
ignore-zero-inf-sign.
* math/auto-libm-test-in: Mark some cpow tests with
ignore-zero-inf-sign and some with xfail-rounding.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (cpow_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch fixes bug 16315, bad pow handling of overflow/underflow in
non-default rounding modes. Tests of pow are duly converted to
ALL_RM_TEST to run all tests in all rounding modes.
There are two main issues here. First, various implementations
compute a negative result by negating a positive result, but this
yields inappropriate overflow / underflow values for directed
rounding, so either overflow / underflow results need recomputing in
the correct sign, or the relevant overflowing / underflowing operation
needs to be made to have a result of the correct sign. Second, the
dbl-64 implementation sets FE_TONEAREST internally; in the overflow /
underflow case, the result needs recomputing in the original rounding
mode.
Tested x86_64 and x86 and ulps updated accordingly.
[BZ #16315]
* sysdeps/i386/fpu/e_pow.S (__ieee754_pow): Ensure possibly
overflowing or underflowing operations take place with sign of
result.
* sysdeps/i386/fpu/e_powf.S (__ieee754_powf): Likewise.
* sysdeps/i386/fpu/e_powl.S (__ieee754_powl): Likewise.
* sysdeps/ieee754/dbl-64/e_pow.c: Include <math.h>.
(__ieee754_pow): Recompute overflowing and underflowing results in
original rounding mode.
* sysdeps/x86/fpu/powl_helper.c: Include <stdbool.h>.
(__powl_helper): Allow negative argument X and scale negated value
as needed. Avoid passing value outside [-1, 1] to f2xm1.
* sysdeps/x86_64/fpu/e_powl.S (__ieee754_powl): Ensure possibly
overflowing or underflowing operations take place with sign of
result.
* sysdeps/x86_64/fpu/multiarch/e_pow.c [HAVE_FMA4_SUPPORT]:
Include <math.h>.
* math/auto-libm-test-in: Add more tests of pow.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (pow_test): Use ALL_RM_TEST.
(pow_tonearest_test_data): Remove.
(pow_test_tonearest): Likewise.
(pow_towardzero_test_data): Likewise.
(pow_test_towardzero): Likewise.
(pow_downward_test_data): Likewise.
(pow_test_downward): Likewise.
(pow_upward_test_data): Likewise.
(pow_test_upward): Likewise.
(main): Don't call removed functions.
* 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.
This patch fixes bug 16349, missing errno setting for atan2 underflow,
by adding appropriate checks to the existing wrappers. (As in other
cases, the __kernel_standard support for calling matherr is considered
to be for existing code expecting existing rules for what's considered
an error, even if those don't correspond to a general logical scheme
for what counts as what kind of error, so __set_errno calls are added
directly without any changes to __kernel_standard.)
Tested x86_64 and x86.
[BZ #16349]
* math/w_atan2.c: Include <errno.h>.
(__atan2): Set errno for result underflowing to zero.
* math/w_atan2f.c: Include <errno.h>.
(__atan2f): Set errno for result underflowing to zero.
* math/w_atan2l.c: Include <errno.h>.
(__atan2l): Set errno for result underflowing to zero.
* math/auto-libm-test-in: Don't allow missing errno for some atan2
tests.
* math/auto-libm-test-out: Regenerated.
This patch fixes bug 16348, spurious underflows from x86/x86_64 expl
on arguments close to 0. These implementations effectively use expm1
(on the fractional part of the argument) internally, so resulting in
spurious underflows when the result is very close to 1. For arguments
small enough that the round-to-nearest correct result is 1, this patch
uses 1+x instead.
These implementations are also used for exp10l and so the patch fixes
similar issues there (the 0x1p-67 threshold being small enough to be
correct for exp10l as well as expl). But because of spurious
underflows in other exp10 implementations (bug 16560), the tests
aren't added for exp10 at this point - they can be added when the
other exp10 parts of that bug are fixed.
Tested x86_64 and x86; no ulps updates needed.
[BZ #16348]
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [!USE_AS_EXPM1L]: Use
1+x for argument with exponent below -67.
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [!USE_AS_EXPM1L]:
Likewise.
* math/auto-libm-test-in: Add more tests of exp.
* math/auto-libm-test-out: Regenerated.
gen-auto-libm-tests presently allows but does not require underflow
exceptions for results with magnitude in the range (greatest
subnormal, least normal].
In some cases, the magnitude of the exact result is very slightly
above the least normal, but rounding in the implementation results in
it effectively computing an infinite-precision result that is slightly
below the least normal, so raising an underflow exception. This is in
accordance with the documented accuracy goals, but results in
testsuite failures.
This patch changes the logic to allow underflows when the mathematical
result is up to 0.5ulp above the least normal (so in any case where
the round-to-nearest result is the least normal). Ideally underflows
in all these cases would be accepted only when an underflow with the
actual result is consistent with the rounding mode (in FE_TOWARDZERO
mode, a return value of the least normal implies that the
infinite-precision result did not underflow so there should be no
underflow exception, for example), so as to match the documented goals
more precisely - whereas at present the tests for exceptions are
completely independent of the tests of the returned values. (The same
applies to overflow exceptions as well - they too should be checked
for consistency with the result, as in FE_TOWARDZERO mode a result
1ulp below the largest finite value should be inconsistent with an
overflow exception and cause a failure with overflow rather than
simply being considered a 1ulp error when overflow is expected.) But
the present patch at least deals with the cases causing spurious
failures so that (a) certain existing tests no longer need to be
marked as having spurious exceptions (such markings in
auto-libm-test-in end up applying to more cases than just those they
are needed for) and (b) log1p can be tested in all rounding modes
without introducing more such failures. This patch duly moves tests
of log1p to ALL_RM_TEST.
Tested x86_64 and x86 and ulps updated accordingly.
[BZ #16357]
[BZ #16599]
* math/gen-auto-libm-tests.c (fp_format_desc): Add field
min_plus_half.
(fp_formats): Update initializers.
(init_fp_formats): Initialize new field.
(output_for_one_input_case): Allow underflow for results up to
min_plus_half.
* math/libm-test.inc (log1p_test): Use ALL_RM_TEST.
* math/auto-libm-test-in: Don't mark some underflows from asin and
atanh as spurious.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
The dbl-64 version of exp needs round-to-nearest mode for its internal
computations, but that has the consequence of inappropriate
overflowing and underflowing results in other rounding modes. This
patch fixes this by recomputing the relevant results in cases where
the round-to-nearest result overflows to infinity or underflows to
zero (most of the diffs are actually just consequent reindentation).
Tests are enabled in all rounding modes for complex functions using
exp - but not for cexp because it turns out there are bugs causing
spurious underflows for cexp for some tests, which will need to be
fixed separately (I suspect ccos ccosh csin csinh ctan ctanh have
similar bugs, just not shown by the present set of test inputs).
Tested x86_64 and x86 and ulps updated accordingly.
[BZ #16284]
* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Use original
rounding mode to recompute results that overflow to infinity or
underflow to zero.
* math/auto-libm-test-in: Don't mark tests as expected to fail for
bug 16284.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (ccos_test): Use ALL_RM_TEST.
(ccosh_test): Likewise.
(csin_test_data): Use plus_oflow.
(csin_test): Use ALL_RM_TEST.
(csinh_test_data): Use plus_oflow.
(csinh_test): Use ALL_RM_TEST.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
In 84ba214c, I removed some redundant sign computations and in the
process, I incorrectly got rid of a temporary variable, thus passing
the absolute value of the input to bsloww1. This caused #16623.
This fix undoes the incorrect change.
This patch moves tests of clog10 to auto-libm-test-in. Note that this
means gen-auto-libm-tests will now depend on the recent MPC 1.0.2
release which added a fix for a bug that made gen-auto-libm-tests hang
for clog10. (It still can't conveniently be used for cacos cacosh
casin casinh catan catanh csin csinh because of extreme slowness of
those functions for special cases in MPC; at least some slow cases of
csin / csinh are fixed in MPC trunk, but not in a release.)
Tested x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of clog10.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (clog10_test_data): Use AUTO_TESTS_c_c.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of fma to auto-libm-test-in, adding the
required support to gen-auto-libm-tests.
Because fma can have exact zero results depending on the rounding
mode, results of fma cannot always be determined from a single value
computed in higher precision with a sticky bit. Thus, this patch adds
support for recomputing results with the original MPFR/MPC function in
the case where an exact zero is involved. (This also affects some
results for cpow; when we start testing cpow in all rounding modes, I
think it will be most appropriate to make those tests use
IGNORE_ZERO_INF_SIGN, since ISO C does not attempt to determine signs
of zero results, or special caes in general, for cpow, and I think
signs of zero for cpow are beyond the scope of glibc's accuracy
goals.)
Simply treating the existing test inputs for fma like those for other
functions (i.e., as representing the given value rounded up or down to
any of the supported floating-point formats) increases the size of
auto-libm-test-out by about 16MB (i.e., about half the file is fma
test data). While rounded versions of tests are perfectly reasonable
test inputs for fma, in this case having them seems excessive, so this
patch allows functions to specify in gen-auto-libm-tests that the
given test inputs are only to be interpreted exactly, not as
corresponding to values rounded up and down. This reduces the size of
the generated test data for fma to a more reasonable 2MB.
A consequence of this patch is that fma is now tested for correct
presence or absence of "inexact" exceptions, where previously this
wasn't tested because I didn't want to try to add that test coverage
manually to all the existing tests. As far as I know, the existing
fma implementations are already correct in this regard.
This patch provides the first cases where the gen-auto-libm-tests
support for distinguishing before-rounding/after-rounding underflow
actually produces separate entries in auto-libm-test-out (for
functions without exactly determined results, the affected cases are
all considered underflow-optional, so this only affects functions like
fma with exactly determined results). I didn't see any signs of
problems with this logic in the output.
Tested x86_64 and x86.
* math/auto-libm-test-in: Add tests of fma.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (fma_test_data): Use AUTO_TESTS_fff_f.
(fma_towardzero_test_data): Likewise.
(fma_downward_test_data): Likewise.
(fma_upward_test_data): Likewise.
* math/gen-auto-libm-tests.c (rounding_mode_desc): Add field
mpc_mode.
(rounding_modes): Add values for new field.
(func_calc_method): Add value mpfr_fff_f.
(func_calc_desc): Add mpfr_fff_f union field.
(test_function): Add field exact_args.
(FUNC): Add macro argument EXACT_ARGS.
(FUNC_mpfr_f_f): Update call to FUNC.
(FUNC_mpfr_f_f): Likewise.
(FUNC_mpfr_ff_f): Likewise.
(FUNC_mpfr_if_f): Likewise.
(FUNC_mpc_c_f): Likewise.
(FUNC_mpc_c_c): Likewise.
(test_functions): Add fma. Update calls to FUNC.
(handle_input_arg): Add argument exact_args.
(add_test): Update call to handle_input_arg.
(calc_generic_results): Add argument mode. Handle mpfr_fff_f.
(output_for_one_input_case): Update call to calc_generic_results.
Recalculate exact zero results in each rounding mode.
gen-auto-libm-tests has a bug in the logic for setting a sticky bit
based on the ternary value from MPFR: it is correct for positive
results, but for negative results mpz_setbit acts as if a two's
complement representation is used, whereas the low bit needs setting
based on the sign-magnitude representation GMP actually uses. (This
showed up in converting fma tests to use auto-libm-test-in /
gen-auto-libm-tests.)
This patch fixes the problem by negating the mpz_t value to set its
low bit. There are lots of changes to auto-libm-test-out (mainly 1ulp
fixes to ldbl-128 expected results), but only a few ulps updates are
needed on x86 / x86_64. In one case, a corrected expectation showed
up a spurious underflow exception where the correct result is slightly
outside the underflowing range.
Tested x86_64 and x86 and ulps updated accordingly.
* math/gen-auto-libm-tests.c (adjust_real): Ensure integers are
non-negative before setting low bit.
* math/auto-libm-test-in: Mark one asin test possibly having
spurious underflow.
* math/auto-libm-test-out: Regenerated.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch marks more libm tests as expected to fail for ldbl-128ibm
in non-default rounding modes. Given this, my expm1l fix
<https://sourceware.org/ml/libc-alpha/2014-01/msg00135.html> and my
libgcc fix <http://gcc.gnu.org/ml/gcc-patches/2014-01/msg00157.html>
for spurious overflows, the remaining failures in test-ldouble.out
(for powerpc32 hard float) are small ulps, spurious underflow and
inexact exceptions (the former probably arising from libgcc bugs
though I haven't checked each case; the latter are barely meaningful
for this format anyway when basic arithmetic isn't correctly rounding,
though most of them are probably GCC bug 59412 which doesn't actually
involve long double), missing underflow exceptions from clog, ctan and
ctanh (probably one of the known bugs for another function), and logb
in round-downward mode (bug 887, though it's really a GCC bug that
we're not currently working around).
Tested for powerpc32 hard float.
* math/auto-libm-test-in: Mark various tests with
xfail-rounding:ldbl-128ibm.
* math/auto-libm-test-out: Regenerated.
This patch marks various libm tests with xfail-rounding:ldbl-128ibm,
where the failures appear to relate to GCC bug 59666 (bad libgcc
handling of directed rounding), so as to allow clean libm-test-ulps
regeneration without needing to edit out large ulps for various
functions manually.
Note that this only deals with the cases problematic for ulps
regeneration. There are plenty of test failures left that do not
affect ulps regeneration - results that are infinities or NaNs but
should be finite, or vice versa, and missing and spurious exceptions -
which should also be resolved during the release testing period.
Tested for powerpc32 (hard float).
* math/auto-libm-test-in: Mark various tests with
xfail-rounding:ldbl-128ibm.
* math/auto-libm-test-out: Regenerated.
